SOVIET ATOMIC ENERGY VOL. 40, NO. 4

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• Document Page Count: 101
• Document Creation Date: December 23, 2016
• Document Release Date: April 10, 2013
• Sequence Number: 4
• Publication Date: October 1, 1976
• Content Type: REPORT

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Russian Original Vol. 40, No. 4, April, 1976
October, 1976
SATFAZ 40(4) 349-444 (1976)
r
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEP('I4H
(ATOMNAYA ENERGIYA)
Ub
CONSULTANTS BUREAU, NEW YORK
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SOVIET
ATOMIC
ENERGY
Soviet 'Atomic Energy is a cover-to=cover translation of Atomnaya
Energiya, a publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency of the;USSR (VAAP)
yinakes available both advance copies of the Russian journal and
original glossy photographs and artwork. This serves,to decrease
.the necessary time lag between- publication of the original sand
publication of the translation and helps to'improve the quality
of, the latter. The translation began--with the first, issie of the
Russian journal.
Editorial Board of Atomnaya 'nergiya:
Editor: M. D.`,Millionshchikov
Deputy Director ! J
I. V. Kurchatov Institute of Atomic Energy
Academy of Sciences of the USSR
Moscow, USSR
Associate Editor: N. A. Vlasov
A..A; Bochvar . ` V. V. Matveev
N. A. Dollezhal' M. G. Meshcheryakov-
V. S. Fursov V. B. Shevchenko
I. N. Golovin V. I. Smirnov
V. F. Kalinin A. P. Zefirov
A. K. Krasin
Soviet Atomic Energy is'abstracted or in-
dexed in Applied Mechanics Reviews, Chem-
ical Abstracts, Engineering Index, INSPEC-
Physics Abstracts and Electrical- and Elec-
tronics Abstracts, Current Contents, and
Nuclear Science Absttracis.
Copyright ?'1976 Plenum Publishing Corp,bration; 227 West 17th Street, New York,
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
October, 1976
Volume 40, Number 4
April, 1976
CONTENTS
Engl./Russ-
ARTICLES
-Plutonium Charging of the VVER-440 Water-Cooled Water-Moderated Reactor
- H. Kaikkonen and P. Silvennoinen ................................ 349 283
esign of Sodium - Water Steam Generators - P. L. Kirillov and V. M. Poplavskii ... 353 286
Nature and Thermal Stability of Radiation-Induced Defects in Zirconium Hydride
- P. G. Pinchuk, V.. N. Bykov, G. A. Birzhevoi, Yu. V. Alekseev,
A. G. Vakhtin, and V. A. Solov'ev. ................................. 356 289
Empirical Relationship between the Swelling of 0Kh16N15M3B Steel and Irradiation
Dose and Temperature - V. N. Bykov, V. D. Dmitriev, L. G. Kostromin,
S. I. Porollo, and V. I. Shcherbak ................................. 360 293
The Adsorption of Krypton and Xenon at Low Partial Pressures on Industrial Samples
of Activated Carbon - I. E. Nakhutin, D. V. Ochkin, S. A. Tret'yak,
and A. N. Dekalova. ............................ ..... ..... 364 295
Total Neutron Cross Section and Neutron Resonance Parameters of 243Am in the Energy
Range 0.4-35 eV - T. S. Belanova, A. G. Kolesov, V. A. Poruchikov,
G. A. Timofeev, S. M. Kalebin, V. S. Artamonov, and R. N. Ivanov ......... 368 298
Total Neutron Cross Section and Neutron Resonance Parameters of 241Am in the Energy
Range 0.004-30 eV - S. M. Kalebin, V. S. Artamonov, R. N. Ivanov,
G. V. Pukolaine,.T. S. Belanova, A. G. Kolesov, and V. A. Safonov ......... 373 303
The Pulsed FLIT-1B Electron Accelerator - Yu. G. Bamburov, S. B. Vasserman,
V. M. Dolgushin, V. F. Kutsenko, N. G. Khavin, and B. I. Yastreva ......... 378 308
Cross Sections of the Interaction of Protons and Electrons with Atoms of Hydrogen,
Carbon, Nitrogen, and Oxygen - V. A. Pitkevich and V. G. Videnskii......... 382 311
Pulsed Neutron Sources for Measurement of Nuclear Constants - S. I. Sukhoruchkin... 390 318
DEPOSITED PAPERS
Asymptotic Neutron Distribution in a Nonmultiplying Two-Zone Cylindrical Medium
- A. L. Polyachenko .......................................... 403 332
Neutron Importance Function in Heterogeneous Reactors - V. A. Dulin ............ 405 333
LETTERS
In-Core System for Automatic Power Control of IRT-M Reactor - L. G. Andreev,
Yu. I. Kanderov, M. G. Mitel'man, N. D. Rozenblyum, V. P. Chernyshevich,
and Yu. M. Shiporskikh ........................................ 407 335
Determination of Irradiation Temperature from Measurement of Lattice Constant of
Radiation Voids - Y. V. Konobeev ................................. 410 337
Slowing Down of Resonance Neutrons in Matter - D. A. Kozhevnikov .............. 412 338
Measurement of a in the Resonance Region - Yu. V. Ryabov ................... 414 339
Ionization Energy Losses and Ranges of Alpha Particles in Ionic Crystals
- G. N. Potetyunko and E. T. Shipatov ............................. 418 343
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CONTENTS
A Monochromatic' Annihilation Gamma-Ray Beam from a .2-GeV Linear Electron
Accelerator - B. I. Shramenko, G. L. Bochek, V. I. Vit'ko, I. A. Grishaev,
V. I. Kulibaba, G. D. Kovalenko, and V. L. Morokhovskii ...:.. . .........
Parameters of Semi-Insulating GaAs Nuclear-Radiation Detectors - S. A. Azimov,
S. M. D'ukki, R. A. Miminov, and U. V. Shchebiot ......................
COMECON DIARY
Sixth International Conference on Mbssbauer Spectroscopy - A. G. Beda ............
BIBLIOGRAPHY
A. A. Moiseev and P. G. Ramzaev - Cesium-137 in the Biosphere - Reviewed by
R. M..Aleksakhin ........ ..................................
INFORMATION: CONFERENCES AND MEETINGS
The Second International Conference on Sources of Highly ,Charged Ions - B. N. Markov.
The Third International Conference on Impulse Plasma with High 0 - S. S. Tserevitinov.
A Soviet - American Project for a Diverter for a Tokamak Reactor - A. M. Stefanovskii.
A Conference on Nuclear Data for Transactinoidal Elements - S. M. K41ebin.......
An International School-Seminar on the Interactions of Heavy Ions with Nuclei and the
Synthesis of New Elements - K. G. Kaun and B. I. Pustyl'nik .............
The Russian press date (podpisano k pechati) of this issue was 3/24/1976.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
Engl./Russ.
421
345
423
346
425
349
428
351
429
352
432
353
436
356
438
357
440
358
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PLUTONIUM CHARGING OF THE VVER-440
WATER-COOLED WATER-MODERATED REACTOR
H. Kaikkonen and P. Silvennoinen
The present delay in the adoption of commercial breeder reactors means that the repeated use of
plutonium in the light-water reactors of the 1980's is a likely outcome. Whereas some plutonium-con-
taining assemblies will probably be used in the BWR reactors [1], in the PWR reactors it will be most
reasonable and economical to use plutonium in all the fuel assemblies [2]. Let us therefore consider the
charging of a VVER-440 reactor with the secondary use of plutonium in all the fuel assemblies and a
specific distribution of plutonium enrichment.
Limitations on the Use of Plutonium in the Active Zone of the VVER-440. The monitoring of reac-
tivity and the distribution of energy evolution are the main problems involved in improving the use of
nuclear fuel containing plutonium. It is essential to keep the characteristics of the active zone the same
as in the case of uranium charging. The problem of determining the necessary "weight" of the control
rods has never been examined, but a system of control rods with neutron traps will clearly not introduce
any limitations into the shutting down of the reactor, since the neutrons will be thermalized and largely
absorbed in the water filling the control assemblies, so that the system will be insensitive to changes in
the neutron spectrum. The "pure" lattice and hexagonal geometry of the active zone of the VVER will
lead to a geometrically simple disposition of the plutonium assemblies, despite the fact that the wider
water gaps between the plutonium assemblies will increase the power evolution peaks. In our calculations
we considered that plutonium fuel was incorporated in the initial fuel charge, for which the differences in
the flux levels of the neutron spectra were the greatest. The results accordingly give a conservative esti-
mate of the use of plutonium under practical recharging conditions.
From the point of view of recharging economics, all the fuel assemblies of the VVER-440 reactor
being recharged should be provided with plutonium, since the incorporation of local plutonium-containing
assemblies reduces the plutonium productivity of the reactor by a factor of 2. Typical problems which
arose in organizing the recharging of the PWR reactor were solved in [3] by using at least three degrees
of enrichment in the plutonium assemblies. We used this arrangement in our present calculations,.
According to calculation, the degree of fuel enrichment in the steady state of recharging amounts to
2.4 and 3.6% for U and Pu, respectively. There is no need to use a plutonium enrichment exactly corre-
sponding of the enrichment of the uranium fuel replaced. The foregoing degree of enrichment eases solu-
tion of the problem of repeatedly using the plutonium and satisfies the requirements imposed upon the fuel
circulation, thus giving additional flexibility. In order to maximize the value of the plutonium, the highly
enriched uranium fuel should be replaced by fuel consisting of oxide mixtures, and the envisaged recharg-
ings should take account of this aspect.
Results of the Calculations. In order to obtain groups of parameters based on the ENDF/B data we
used the computer programs FORM [4] and THERMOS [5]. The differential diffusion computing program
TRIGON [6] designed for a triangular lattice configuration was used with two neutron-energy groups in the
general reactor calculations, while four neutron-energy groups were used in the calculation for the fuel
assembly. The boundary of the thermal neutrons was increased to 2.53 eV.
State Technical Scientific-Research Center. Laboratory of Nuclear-Power Technology, Helsinki,
Finland. Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 283-286, April, 1976. Original
article submitted July 4, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication maybe reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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Fig. 1. Distribution of energy evolution in a plutonium fuel assembly contain-
ing fuel with three degrees of enrichment and boron (800 ppm).
Local peaks of energy evolution and interaction between neighboring uranium fuel assemblies were
studied by placing the plutonium assemblies in a position in which they were surrounded by uranium
assemblies with enrichment factors of 1.6 and 2.4% and analogous plutonium assemblies (Fig. 1). In the
plutonium assembly the fuel elements lying along the outer water gap contain 2.15% PU02 and the remain-
der 3.5%. The four inner fuel-element hexagons contain 4.3% PuO2. The enrichment of the whole assem-
bly with respect to fissile plutonium is 4.3%. The two contiguous plutonium assemblies in Fig. 1 are iden-
tical with the central assembly.
In the configuration illustrated in Fig. 1, if the plutonium assemblies are replaced by uranium with
a 3.6% enrichment we shall obtain a maximum relative heat-evolution peak (equal to 1.24) in the corner
adjacent to the fuel with the 1.6% enrichment. On the other hand, if the three plutonium assemblies have
the same PU02 content, equal to 3.5%, the relative heat-evolution peak will increase to 1.59, arising from
the thermal neutron flux of the uranium fuel, in which this flux is considerably higher. This peak is due
to the thermalization of the neutrons in the water gap.
In view of the high level of local heat evolution it is essential to change the enrichment inside the
fuel assembly. A reduction of the plutonium content in the outer elements of the fuel assembly only will
lead to a considerable change of neutron flux in the fifth hexagonal ring of the fuel elements and make it
essential to use a third enrichment factor.
It follows from Fig. 1 that a relative heat-evolution peak of 1.28 occurs in the fuel elements at the
boundary between the plutonium and uranium fuel assemblies. In any practical construction it would even
be desirable to use a fourth plutonium enrichment factor, which would require a corresponding rotation
of the fuel assembly when the fuel is recharged or transposed.
When studying the general energy pattern we considered the replacement of the highly enriched uran-
ium by plutonium fuel. In so doing we investigated possible specific changes in the use of the nuclear
fuel, established the required indices of the active .zone, and also determined the relative value of the
fissile plutonium by comparison with 235U in the lattice of the VVER-440 reactor.
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Fig. 2. Distribution of heat evolution in a group of heat-evolving assem-
blies (1/12 part of the total symmetry) containing uranium and plutonium
fuel and boron (800 ppm) Keff = 0.98824: 1) 1.41 wt. % 235U; 2) 2.14 wt.
fissile Pu; 3) 3.40 wt. % fissile Pu; the numbers in the cells represent the
relative energy distribution.
Plutonium fuel gives a greater depth of burnup than uranium. Certain changes must therefore be
made in the order of using the nuclear fuel. We shall consider an "open" commercial situation in which
there are no restrictions on the use of the plutonium loaded into the reactors. (The opposite situation is
that of a closed fuel cycle in which the consumption of plutonium is limited by its production.) It was found
that the active zone of the VVER-440 offered great possibilities in the breeding of plutonium. Figure 2
illustrates a lattice in which all the fuel assemblies except those in which the lowest uranium enrichment
is employed are replaced by plutonium-containing versions. Economy in separation processes suggests
replacing the highly enriched uranium by plutonium, but at the same time flexibility and the high cost of
making plutonium assemblies dictates the use of poorly enriched uranium in the active zone.
The general distribution of energy evolution is shown in Fig. 2, from which we see that an acceptable
distribution of heat evolution may be obtained in the active zone in the manner indicated. The radial non-
uniformity coefficient is 1.294, which is usually an acceptable figure for a PWR reactor.
Our study has been limited to a neutron-physical analysis of the active zone in the presence of a
" fresh" charge. Allowing for the disposition of the fuel assemblies this reflects a reasonably practical
situation. The difficulties associated with local peaks of energy evolution may be quite easily overcome
by using different fuel enrichments inside the assembly.
Our example of the charging of the active zone with plutonium is of a hypothetical character, since
there is far more plutonium in this arrangement than is required in any practical situation. The calcula-
tions show that there are no problems as regards the distribution of heat evolution with respect to the
radius of the active zone.
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It would be extremely desirable to pursue this investigation with due allowance for the factors in-
volved in the burnup of the nuclear fuel. Certain experimental work will be required in this connection
so as to provide confirmation of the validity of the computer calculations. The nonuniformity of the dis-
tribution of energy evolution will be smoothed as the nuclear fuel is impoverished during burnup.
Another important aspect to be studied is that of determining the "weight" of the control rods. We
feel that a study of reactivity problems will reveal some. more rigorous limitations than those deduced
from the study of energy distribution undertaken in the present investigation.
1. R. Crowther et al., Trans. Amer. Nucl. Soc., 18, 297 (1974).
2. Generic Environmental Statement on the Use of Recycle Plutonium in Mixed-Oxide Fuel in LWRs,
USAEC, WASH-1327 (1974).
3. D. Call and P. Lacey, -Trans. Amer. Nucl. Soc., 19, 347 (1975).
4. P. Siltanen, FORM; A Multigroup Code for Calculating the Fundamental Mode Flux and Current
Spectra of Fast Neutrons, Techn. Res. Center of Finland, Nucl. Engng. Laboratory, Rep. No. 6
(1973).
5. J. Saastamoinen and F. Wasastjerna, THERMOS-OTA, A Revised Version of the THERMOS Pro-
gram for Thermal Lattice Calculations with the Auxiliary Programs THEPSL and THECOM, Techn.
Res. Center of Finland, Nucl. Engng. Laboratory, Rep. No. 10 (1974).
6. E. Kaloinen, A Two-Dimensional Multigroup Diffusion Code for Trigonal or Hexagonal Mesh,
Techn. Res. Center of Finland, Nucl. Engng. Laboratory, Rep. No. 1 (1973).
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P. L. Kirillov and V. M. Poplavskii UDC 621.181.021:621.039.517.5
Various possible constructions of sodium - water steam generators have now been established, but
the terminology has not yet been settled, and this causes certain difficulties .when discussing design prob-
lems and also in the preparation of technical translations, as clearly revealed in the recent steam-genera-
tor seminar (Proc. Development of Sodium-Cooled Fast Breeder Reactor Steam Generators, Los Angeles,
Vol. 1, 1974).
The construction of steam generators for nuclear power stations with fast reactors cooled by liquid
sodium is being developed in two directions.
The first is characterized by shell constructions in which the principal characteristics are: the in-
corporation of shells having dimensions matching the thermal power of one reactor loop; no parallel con-
nection of the shells; the impossibility of disconnecting any shell without infringing the technological basis
of the loop. Each shell is capable of executing one or several functions such as economizer, evaporator,
steam superheater, and intermediate superheater; it may combine two or even all these elements. If the
shell combines all the elements, it will characterize the integral (one-shell) construction (Fig. 1a). If
the shell is divided into several parts we shall have the two- or three-shell construction (Fig. 1b, c). *
The second direction is that of section-type (module) constructions with the following main character-
istics: sections connected in parallel; the combination of all functional elements of the steam generators
in one or several modules; the fact that the disconnection of one or even several sections does not lead to
the stopping of the whole steam generator. A section may be made in one-, two-, or three-module form
(Fig. 2a, b, c) and so on.
*In the captions to Figs. 1 and 2 the proposed terminology is given in four languages.
Fig. 1. Korpusnyi Shell-type steam
parogenerator generator:
a) integral'nyi integral
(odnokorpusnyi) (one-shell)
b) dvukhkorpusnyi two-shell
c)trekhkorpusnyi three-shell
Corps type generateur Korpus Typ
de vapeur: Dampferzeuger:
type integre integrierter
(un corps) (ein Korpus)
deux corps zwei Korpusse
trois corps drei Korpusse
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 286-288, April, 1976. Original article
submitted May 4, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfrhning,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for 515.00.
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Fig. 2. Sektsionnyi
(modul' nyi)
parogenerator:
a) integral' naya
sektsiya
(odiiomodul' naya )
b) dvukhinodul'naya
sektsiya
c) trekhmodul'nay.a
sektsiya
Section-type (mo- Section type Sektion Type
dule type) steam generateur de Dampferzeu-
generator: vapeur: ger:
integral integral integrierte
(one module) (un module) Sektion
(ein Modul)
two-module deux-modules zwei Modul-
Sektion
three-module trois-modules drei Modul-
Sektion
A section is a part of the steam generator comprising one or several modules capable of being dis-
connected simultaneously.
A module is an individual construction element, technologically perfected under workshop conditions,
possessing the characteristics of a heat exchanger (shell, heat-transfer elements, inlet and outlet coolant
chambers, and so forth). A module may have a specific purpose (economizer, evaporator) or combine
several elements, i.e., it., may constitute a combined module.
Modules may be classified by dimensions: micromodules (1 MW), low-power modules (1-10), me-
dium (10-100), and high-.power modules (over 100 MW). Shell-type steam generators have the following
advantages: compactness, low specific cost, low metal requirements, inexpensive assembly, and a min-
imum number of instruments.
The shortcomings of shell-type steam generators include: complication of manufacturing technology
due to their large size; greater time of manufacture and complexity as regards conservation, difficulty in
finding defective elements under working conditions; the essential disconnection of the whole loop for re-
pairing the steam generator when a single tube develops a fault; the impossibility of determining the con-
sequences of leak development, and hence the impossibility of prolonging operation after the removal of a
leak. There are grounds for considering that as a result of the interaction of sodium with water the mate-
rial of neighboring tubes may undergo serious structural changes in the case of substantial leaks, and
damage right through if small leaks occur.
The advantages of section-type (module) steam generators include: simplicity of manufacturing
technology; the possibility of checking the thermohydraulic characteristics under test-bed conditions
directly on full-size modules; great reliability because of the possibility of localizing any emergency
within a single module should a particular tube suffer damage; the possibility of continuing work when
other modules fail; the moderate cost of the module.
The disadvantages of sectioned (module-type) steam generators include: less compactness than that
of shell-type systems; greater size and total amount of metal, high total cost; greater complexity (col-
lectors, fittings, instruments); possible flow misalignment when operating with a large number of parallel
channels; higher pressures when the sodium and water interact.
The development of a new type of steam-generator, construction has recently been proposed; in this
the sodium flows through tubes, and a vapor - liquid mixture occupies the intertube space. Such construc-
tions are called "inverted" steam generators; their main advantage is the restriction of the area of the
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emergency if a leak develops and the sodium comes into contact with water. The reaction region is taken
out of the piping and into the inlet and outlet chambers; neighboring tubes remain undamaged. Another
advantage is the pressure outside the tubes, which reduces the stresses in the walls at the water interface.
Shortcomings of this construction are as follows: the difficulty of finding a leak and restoring the
system following the opening of the sodium space and preliminary purifications; the possibility of fissure
corrosion at the points at which the tubes are fitted into the tube board; possible instability of the hydrau-
lic characteristics of the two-phase mixture and the thermal state of the walls, owing to the low mass
velocities in the intertube space.
In order to obtain experience and establish the positve and negative features of this construction, a
great deal of design and experimental work will have to be carried out.
At the present time shell-type steam generators have been made in the EFFBR (USA), PFR (UK),
and BOB and BN-350 installations (USSR), and sectional steam generators in the EBR-II (USA), Phenix
(France), and BOR and BN-600 (USSR).
As yet, however, there is no single opinion as to the best form of sodium- water steam generator
for the fast-reactor nuclear power stations of the immediate future. This is chiefly because of a lack of
service experience.
British, French, and Italian specialists are largely inclined toward shell-type steam generators for
high-power reactors. Soviet and United States scientists consider that section-type (module) steam genera-
tors have sufficient advantages.
Operating experience accumulated in the Soviet Union during the manufacture of the steam genera-
tors for the BOR-60 and BN-350 installations, as regards experimental construction, the development of
manufacturing technology, assembly, conservation, adjustment, and practical use, has shown that the
section-type steam generator will be the best for the immediate future as regards providing the greatest
degree of safety together with adequate efficiency (the steam generator being kept in action during leakage).
The choice of the number of sections and the number of modules in each section will have to be based on
economy as well as safety and efficiency.
In order to realize the advantages of section-type construction it is essential to create an effective
system of emergency protection, such as to increase the serviceability of the steam generator very sub-
stantially and reduce the danger of leaks.
There is at present a clear need to develop objective criteria for assessing the merits of various
steam-generator constructions. These criteria will certainly incorporate the cost of the steam generator
and its running expenses.
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NATURE AND THERMAL STABILITY OF
RADIATION-INDUCED DEFECTS IN
ZIRCONIUM HYDRIDE
P. G. Pinchuk, V. N. Bykov,
G. A. Birzhevoi, Yu. V. Alekseev,
A. G. Vakhtin, and V. A. Solov'ev
The influence of gaseous elements introduced into the lattice of a metal on the character and stability
of its radiation-induced defects is being widely studied at the present time [1]. It is interesting to study
the nature and annealing of the defects in irradiated interstitial phases having a metalloid sublattice con-
sisting of atoms of gaseous elements. In the present investigation we studied the nature and annealing of
defects in zirconium hydride ZrH1,9 irradiated at 50?C with an integrated flux of 3.2 .1021 neutrons/cm2
(1.8.1020 neutrons/cm2 with energies of over 1 MeV) by measuring the density d, electrical resistance
P, microhardness H?, and lattice constants a and c at 25?C and also the thermal conductivity A at 100?C
(Table 1). In determining the lattice thermal conductivity Ap = X - (LT/p) in which the Lorentz constant
L = 2.45.10-8 W ?S2/deg2, the values of p were reduced to a temperature of 100?C. Isochronous annealing
was carried out at 50-600?C with a holding period of 1 h, and isothermal annealing at 325?C for up to 1000
min.
Results of the Investigations. Following the irradiation of the hydride, the hydrogen content CH =
H/Zr (determined by the thermal-decomposition method), the type of crystal lattice (face-centered tetra-
gonal), and the microstructure remained constant, but the lattice constant c increased, while the lattice
constant a, the degree of tetragonality, and the unit-cell volume all diminished. No vacancy pores or
dislocation loops were observed on studying a ZrH1,9 sample irradiated with 1.8 .1021 neutrons/cm2 at
50?C under the electron microscope at a magnification of 105.
The curves representing the changing properties of samples irradiated with up to 3.2.1021 neutrons/
cm2 during the annealing process (Figs. 1 and 2) were plotted from the experimental points by means of a
piecewise polynomial approximation, using segments of cubic parabolas [2], while the recovery spectra of
the properties (Fig. 3) were obtained by differentiating the original curves. The increment in electrical
resistance found after annealing at 80?C (a single point) was anomalous and was disregarded in the analysis.
The concentration of hydrogen vacancies, i.e., free tetrahedral pores (Fig. 2), was determined as CH =
[(2-Cg)/2] 100% where C 1 was found from the curves relating the lattice constants a and c to the hydro-
gen content [3].
TABLE 1. Change in the Properties of the Hydride ZrH1,9 as a Result of irradiation with
State of sample I
AP
sa vcm , %
+
d,g/cm2
ed
a ' %
?H?'
kg /mm2 H % I
%
w/m . de~
ea J,
' p
?
Original
Irradiated
35,5
88,2
-
148
5,612
5,539
-
-1,31
147
216
-
47
18,6
4,9
-
-74
0,895
1,909
Mean-square measuring
0,5
-
0,1
-
4
-
5,5
-
0,1
error
an Integrated Flux of 3.2 .1021 Neutrons/cm2 at 50?C
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 289-292, April, 1976. Original article
submitted July 9, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means; electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
7,905
tl
07901
Fig. 1 Fig. 2
Fig. 1. Change in the physical properties of the irradiated hydride during
isochronous annealing for 1 h (a, b, c): a) resistivity Op = pirr pnonirr
at 25?C; b) hydrostatic density Ad = dirr - dnonirr; c) microhardness 0H? =
H?irr - H?nonirr; d) phonon component of thermal conductivity at 100?C.
Fig. 2. Recovery of the changes in lattice constants, the degree of tetra-
gonality of the irradiated sample, and the concentration of hydrogen vacancies
during the isochronous annealing of the irradiated hydride for 1 h (a, b, c):
a) Aa = a?rr - anonirr; b) Ac=cirr-cnonirr; 0) Aa, A; A) Ac, A; c)
ACH_ Ci - CH
v virr v nonirr
The curves of Figs: 1-3 exhibit three stages in' the recovery of the properties in question (1-3); the
corresponding temperature intervals appear in Table 2. At temperatures above 540?C we notice the be-
ginning of the next stage. The activation energy Q characterizing the recovery of the properties was de-
termined by a method based on combined isochronous and isothermal annealings [4] in the case of the elec-
trical resistance, and also by reference to the recovery spectra in that of all the other properties, using
the formula Q = 2.5 k0(Ta/T) derived in [5], where TO is the temperature of maximum recovery rate of
the properties in ?K; AT is the width of the peak at half height; and k is Boltzmann's constant.
Discussion of the Results. Since vacancy pores were formed in the hydride as a result of irradia-
tion at 50?C, while the unit-cell volume diminished, the 1.31% swelling of the samples originally observed
must have been due to the accumulation of a corresponding number of isolated zirconium vacancies or
small complexes of these (:510 A).
It is well known that the tetrahedral pores in the metallic sublattice of zirconium hydride are the
nodal points of its hydrogen sublattice. In the hydrogen-saturation of zirconium, the filling of the tetra-
hedral pores with hydrogen in the F-region of the Zr - H diagram is accompanied by an increase in lattice
tetragonality [3]. Irradiation reduces the tetragonality, and this may be interpreted as being due to the
transition of hydrogen from the tetrahedral pores to the octahedral pores or defects in the metallic sub-
lattice. The influence of the latter on the tetragonality cannot be discounted, although in this case the
changes in a and c will take place in the same direction. The increase in the tetragonality of the hydride
on annealing is equivalent to the filling of the tetrahedral pores on saturating with hydrogen. The change
in the tetragonality of the hydride on irradiation appears to be mainly associated with the accumulation of
defects in the hydrogen sublattice.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP1O-02196ROO0700070004-7
TABLE 2. Characteristics of Various
Stages in the Recovery of Z rH1,9 Prop-
erties
Q, eV
Property
Temperature
?
Ta. K
I
by meth-l by meth
od of [5] od of [4]
C
range,
59-290
290-440
470
650
0,3
1,30
0,2
1,53
P
440-540
755
1,40
1,55
50-270
460
0,3
-
d
270-430
I
645
1, 28
-
430-540
755
1,9
-
C
.-
250-415
590
0
0 72
I
a
415-540
I 750
1,32
7 P
I 310-450
660
1,28
-.
Our investigations into ZrH19 9 samples irradiated with a
100 200 300 400 500 7 , ?c
Fig. 3. Recovery spectra of the
resistivity, hydrostatic density,
and microhardness, the phonon
component of the thermal conduc-
tivity, and the lattice tetragonality
during the isochronous annealing
of the irradiated hydride (relative
units).
dose of 6.2. 1021 neutrons/cm2 at 480?C showed that the density,
microhardness, and lattice thermal conductivity changed by -2.4,
+79, and -34% respectively, while the increment in electrical
resistance was +32%; the change in the tetragonality lay within
the limits of experimental error. A comparison between these
results and the data of Table 1 shows that defects in the metallic
sublattice are responsible for the changes in density, lattice
thermal conductivity, and microhardness, and also for some of
.the increase in electrical resistance, which is in toto due to de-
fects in each of the sublattices.
The activation energy Q = 0.27 f 0.05 eV at the first stage
in the recovery of the properties agrees closely with the migra-
tion energy of interstitial atoms in fcc metals [6]; the activation
energy at the second and third stages (1.35 0.1 and 1.54 + 0.2
eV respectively) agrees with the activation energy of zirconium
self-diffusion (1.2-2.2 eV) [7, 8] and that of the diffusion of zir-
conium in the hydrides ZrH166-17 7 (1.1-1.7 eV) [9]. A character-
istic feature of zirconium is the similarity between the self-
diffusion activation energy and the energy of vacancy migration,
since the concentration of the latter in the metal is almost always
sufficient to guarantee a diffusion process [10]. This is evidently
also true of zirconium hydride, especially after irradiation.
Assuming that the sequence of the annealing stages for the metal
sublattice defects in the hydride is the same as in metals [5,11 ],
we may conclude that at the second stage the zirconium vacancies
migrate, while at the third stage the complexes of defects are
annealed. The slight reduction in swelling at the second stage
is evidently associated with the fact that most of the migrating
vacancies form cavities.. The activation energy for the recovery
of the lattice tetragonality at the second stage (0.72 eV) coincides
with the migration energy of hydrogen [12], while the temperature
corresponding to the maximum rate of recovery is in this case
55-70? lower than in the recovery of the other properties. Evidently at the second stage the recovery of
the hydrogen sublattice takes place in advance of the annealing of the zirconium vacancies.
At the third stage the complex defects formed in the course of annealing (and possibly during irradia-
tion) vanish. The recovery of the hydrogen sublattice now occurs within the same temperature range, and
with the same activation energy, as the annealing of defects in the metallic sublattice. Evidently some of
the displaced H atoms occur in complexes of zirconium vacancies and are released when these decompose.
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After annealing at 600?C the hydrogen sublattice is completely restored (according to c/a measure-
ments) but changes of 62-% in density, 1000/0 in microhardness, and 26% in electrical resistance remain intact.
The microhardness recovery curve of the irradiated hydride exhibits two maxima lying at 180 and
450?C; this is due to the formation of complexes during the migration of point defects similar to those
formed in zirconium and Zircaloy after irradiation or quenching [13, 141. The rise in H? close to 200?C
is associated with the formation of defect aggregates, while the peak at 450?C is associated with the for-
mation of prismatic dislocation loops b = (a/3) [1120]. The agreement between the microhardness peaks
found in [13, 14] and in the present investigation suggests that the peak at 180?C corresponding to the first
stage in the recovery of the properties is associated with the formation of aggregates of interstitial zir-
conium atoms, while the peak at 450?C (boundary between the second and third stages) is associated with
the formation of vacancy cavities, and not dislocation loops, as in zirconium, since the reduction in
swelling associated with the annealing of the vacancies is very insignificant in this region.
The face-centered ZrH1,9 lattice with its small degree of tetragonality resembles the lattice of fcc
metals, in which five stages of defect annealing are known to occur (I- V). Stage III is often explained as
being due to the migration of interstitial atoms and has a maximum at 0.215Tm; stage IV is due to the mi-
gration of vacancies at 0.29 Tm; stage V is due to self-diffusion beginning at 0.33Tm [11]. If we assume
that these same values correspond to. the analogous characteristic temperatures of zirconium hydride,
then according to Table 2 we obtain Tm ZrH1,9 = 2155 t 75 ?K which is close to Tm (Zr) = 2125 ?K. This
agrees with the experimental fact that the melting points of zirconium and zirconium hydride differ by only
7-8% [15].
CONCLUSIONS
1. On irradiating ZrH19 9 with an integrated flux of 3.2 ?1021 neutrons/cm2 (1.8. 1020 neutrons/cm2
with energies over 1 MeV) at 50?C, zirconium vacancies accumulate, possibly together with small vacancy
complexes (=10 A) and also defects in the hydrogen sublattice. The defects of the metallic sublattice
cause swelling, an increase in hardness, and increased thermal and electrical resistance. The defects
of the hydrogen sublattice increase the electrical resistance and reduce the lattice tetragonality.
2. The recovery of the properties on annealing the irradiated hydride at 50-540?C takes place in
three stages; the first is associated with the migration of interstitial atoms, the second with vacancy
migration, and the third with the annealing of complex defects.
There are two temperature ranges of complex-formation: Close to 180?C aggregates of interstitial
atoms are apparently formed, and at 270-450?C vacancy cavities (voids).
3. The recovery of the hydrogen sublattice takes place in the second and third stages.
4. The melting point of zirconium hydride (Tm = 2155 ? 75 ?K) may be estimated by comparing the
annealing temperatures of similar defects in the hydride and fcc metals.
The authors wish to thank V. I. Shcherbak for great help in the electron-microscope investigations.
1. D. Norris, Radiat. Effects, 15, No. 1-2, 1 (1972).
2. M. Yu. Orlov, Preprint Physical Power Institute TR-1011 [in Russian], Obninsk (1972).
3. P. Paetz and K. Lucke, Z. Metallkunde, 62, No. 9, 662 (1971).
4. C. Meechan and J. Brinkmen, Phys. Rev., 103, No. 5, 1193 (1956).
5. R. V. Baluffi et al., in: Recovery and Recrystallization of Metals [in Russian), Metallurgiya,
Moscow (1966), p. 8.
6. A. C. Damask and J. G. Dienes, Point Defects in Metals, Gordon (1964).
7. V. S. Lyashenko, V. N. Bykov, and L. V. Pavlinov, Fiz. Metal. i Metalloved., 8, No. 3,362 (1959).
8. E. V. Borisov, in: Metallurgy and Metallography [in Russian], Izd. AN SSSR (1958), p. 291.
9. G. Bentle, Amer. Ceram. Soc., 50, No. 3, 166 (1967).
10. G. Kidson, J. Phys. Chem. Solids, 26, No. 7, 1853 (1965).
11. J. Nihoul, in: Proc. Symp. IAEA Radiation Damage in Reactor Materials, Vol. 1, Vienna (1969); p.3.
12. P. Paetz and K. Lucke, Z. Metallkunde, 62, No. 9, 657 (1971).
13. D. Lee and E. Koch, J. Nucl. Mater., 50, No. 2, 162 (1974).
14. K. Snowden and K. Veevers, Radiat. Effects, 20, No. 3, 169 (1973).
15. J. Lakner, Chem. Engng. News, 39, 39 (1961).
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
EMPIRICAL RELATIONSHIP BETWEEN THE
SWELLING OF 0Kh16N15M3B STEEL AND
IRRADIATION DOSE-AND TEMPERATURE
V.
N.
Bykov, V. D. Dmitriev,
L.
G.
Kostromin, S. I. Porollo,
and
V.
I. Shcherbak
In this paper we shall present the results of an investigation into the swelling of 0Kh16N15M3B
steel used for the fuel element cans in the carbide zone of the BR-5 reactor [1, 2].
For an electron-microscope study of the radiation-induced swelling of 0Kh16N15M3B steel we used
fuel-element cans of both working (G-5, G-6, G-17, and G-19) and experimental (EP-10, EP-11, and
EP-19) packs. The test samples were cut from various cross sections of the fuel-element cans and irra-
diated at 430-590?C with a neutron flux of (0.7-4.35) ? 1022 neutrons/cm2.
Before irradiation the fuel-element cans were annealed at 950?C for 10 min. A study of the cans in
nonirradiated packs made from this steel showed that this kind of heat treatment led to the development of
an initial dislocation density of (4 f 2) ? 1010 cm 2.
The results of an analysis of the electron micrographs obtained from the test samples are presented
in Table 1, together with the condition of irradiation.
A comparison between experimental results obtained for the swelling of materials irradiated with
neutrons of varying spectral characteristics is only valid if the numbers of atomic displacements Kt are
counted in each particular case. Table 1 gives the values of Kt calculated on the basis of the model pro-
posed in [3]. The neutron spectrum for the BR-5 reactor, and the values of the scattering cross sections
are taken from [4].
It should be noted that at the present time various research workers use a number of other models
for calculating the number of displacements [5-9]. Table 2 shows the K values calculated for the center
of the active zone in the BR-5 reactor by some of the most widely employed models. The K calculations
carried out for various points of the active zone showed that the main difference in all these models simply
amounted to a change in the absolute value of K, while the manner in which the rate of displacement varied
over the radius or height of the active zone of the reactor was practically the same for all the models in
question. For a relative comparison between the experimental results any of these models may therefore
be used.
Experimental observations showed that the relative increase in the volume of the steel was mainly
determined by the irradiation dose and temperature. As regards the effect of the rate of creation of the
displacements, it was shown in [10] that a 10-times change in the neutron flux intensity had no effect on
the swelling of austenitic steels.
The relationship between the volume increment of the material (as a result of porosity development)
and the irradiation dose and temperature may be expressed in the following way
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 293-295, April, 1976. Original article
submitted July 16, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication maybe reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
TABLE 1. Conditions Governing the Irra-
diation and Swelling of OKh16N15M3B Steel
No, of
pack
Neutron [Dose,
flux ?.
22 displace-
10 , - menu/
cm tons I atoms
Irradia-
tion
tem C
p'
S
exp
%
S
talc
p -19
0,7
6,8
430
0,07
0,09
Y17
1,8
18,0
430
0,25
0,27
19
2,0
19,9
430
0,30
0,3
P
-10
2,05
20,5
430
0,34
0,32
G_6
2,2
21,5
430
0,35
0,35
P -19
0,8
8,6
440
0,10
0,12
P -19
0,9
9,8
442
0,11
0,15
P-19
0,9
9,8
445
0,12
0,15
P-19
0,9
9,8
447
0,12
0,16
P .19
0,9
9,8
450
0,13
0,16
G-19
3,05
28,4
470
0,86
0,82
IP-19
0,95
10,0
470
0,18
0,19
G-17
2,95
31,5
475
0,74
0,97
G-19
3,05
28,4
475
0,90
0,83
G-6
3,5
37,4
475
1,29
1,24
G-17 ,
2,95
31,3
480
0,6
0,96
G-6
3,5
37,4
480
1,28
1,25
G-17
2,95
31,3
485
0,8
0,97
G-6
3,5
37,4
485
1,22
1,25
G-17
2,95
31,3
490
0,75
0,96
G.6
3,5
37,4
490
1,14
1,23
G-17
3,6
39,1
500
0,88
1,20
G-17
3,6
39,1
505
0,94
1,15
G-17
2,9
31,0
505
0,78
0,83
G5
2,55
26,3
505
0,60
0,67
G-6
4,35
46,8
505
1,50
1,45
-17
3,6
39,1
515
1,10
1,07
P-19
1,35
14,7
520
0,27
0,23
G-5
1,65
15,8
520
0,34
0,25
G-5
2,95
34,3
520
0,87
0,70
G-6
3,5
32,9
520
1,16
0,75
G-6
4,35
46,8
520
0,94
1,13
G-19
3,8
43,6
520
1,40
1,27
G-17
2,90
27,3
530
0,38
0,46
G-17
3,6
39,0
530
1,10
0,80
6
4,35
46,8
530
1,20
1,03
-19
2,2
12,8
535
0,12
0,13
P-19
1,35
14,7
535
0,15
0,16
P-19
1,2
12,8
540
0,11
0,11
G-5
1,65
15,8
540
0,15
0,15
G-17
2,95
31,3
540
0,24
0,42
G-17
3,6
39,1
540
0,42
0,60
G-6
3,5
32,9
540
0,28
0,47
P-10
4,15
44,4
540
0,47
0,72
P 19
1,2
12,8
545
0,12
0,091
P-19
1,35
14,7
545
.0,13
0,11
G-17
3,6
39,1
545
0,30
0,51
G-6
4,35
46,8
545
0,67
0,66
P-10
4,15
44,4
550
0,33
0,5
5-17
2,90
27,3
550
0,09
0,24
EP-19
1,2
12,8
555
0,09
0,06
17
2,90
27,3
555
0,10
0,19
P-19
1,05
12,2
570
0,02
0,02
G19
2,95
31,3
570
0,07
0,10
G-17
2,95
31,3
580
0,03
0,05
G-6
3,5
32,8
580
0,08
0,06
TABLE 2. Values of K, Kt, and u for
Various Models
No, of displacements
x?to7,e
displacemnts/
corresponding to 13
neutron flux2of 10
Litera-
ture
atom , sec
neutrons/cm
(E > 0.1 MeV)
6.1
132,3
0,92
[5]
5,6
121,2
1,00
[3]
4,3
93,0
1,30
[li]
3,9
84,3
1,44
171
3,1
67,1
1,81
[8]
2,8
60,6
2,0).
[9]
where g(T) and f(Kt) are functions describing the swell-
ing as a function of temperature and irradiation dose.
The problem of finding the empircal dependence of S on
T and Kt thus usually amounts to the determination of
g(T) and f(Kt).
In the first case we may take one of the following
functions :
exp (T -r T
expT+expT [12];
exp (a,l+a2T,-[ T ) [13];
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
Temperature Number
range `of points
AS
AS/S, % I as
430-450
10
0,06
31
0,18
470-490
10
0,15.:
17
0,11
510-530
11
0,17
20
0,24
535-550
13
0,12
45
0, 12
555-580
5
0,15
200
0,20
(K, t)ai+a2/T-0+a3/(T-0)2 [13 141?
(K, t)ai+a2T
These functions also correspond better to the real dose dependence of the swelling than the linear
dependence of S on Kt used in [15].
exp / a1T +-- a2 + a3
l T-T2 T2-T
where a1, a2, a3, T1, and T2 are parameters of the
equation. In our own opinion these functions should
give a better idea of the real dependence of S on the
irradiation temperature than an expression in the form
of polynomials [15].
For the function f(Kt) we may assume a power law
of swelling, the power index in turn depending on the ir-
radiation temperature:
(2)
The choice of functions for describing the swelling is made by a computer analysis of the experimen-
tal results indicated in Table 1. Trial of the first and second functions showed that the swelling of 0Kh16-
N15M3B steel in the temperature and irradiation dose range studied could be reasonably described by the
equation
S = 5.33.10-7 ((zKT)0.19+'.03.10-3T
X exp (0.0235T - 8.35 - 17.82.102
T-630 980-T
where T is the temperature in ?K.
Since research workers are at present using a number of different models for calculating Kt, the
parameter a has been introduced into the empirical equation so as to allow the use of several of these.
The values of the conversion factor a corresponding to some of the models most widely used in calculat-
ing the numbers of displacements are given in Table 2.
It should be noted that for an irradiation temperature T equal to Ti or T2 the swelling of OKh16N15M3B
steel becomes equal to zero. These temperatures may therefore be taken as the lower and upper limits of
swelling.
In analyzing any empirical equation, its reliability and error always have to be considered. Table 3
gives the values of the relative errors (AS/S), the confidence intervals (AS) for a confidence probability of
0.9, and the mean square errors of the power index associated with the dose ((Ta) for several temperature
ranges.
We see from this table that the relative error S depends very considerably on the temperature and
is lowest in the range 500 + 30?C.
Extrapolation of the experimental data to an integrated flux of 1023 neutrons/cm2 (Table 2) shows that
.the swelling of OKh16N15M3B steel may extend to 7-8%.
The authors are deeply indebted to A. A. Proshkin, A. N. Tuzov, and A. G. Kostromin for help in
this work.
LITERATURE CITED
1.
V. N. Bykov et al., At. Energ., 34, No. 4, 247 (1973).
2.
V. N. Bykov et al., At. Energ., 36, No. 1, 24 (1974).
3.
J. Jenkins, Nucl. Sci. and Engng., 41, 155 (1970).
4.
N. N..Aristarkhov, V. V. Bondarenko, and A. I. Voropaev, in: Transactions of the Physical Power
Institute [in Russian], Vol. 1, (1967), p. 267.
5.
G. Kinchin and R. Pease, Rep. Prog. Phys., 18, 1 (1955).
6.
E. Ohmae and B. Hida, J. Nucl. Mater., 42, 85 (1972).
7.
D. Dovan,
Nuci. Sci. and Engng., 49, 130 (1972).
8.
R. Nelson,
E. Etherington, and M. Smith, UKAEA,Rep. TRG-2152 (D) (1971).
9.
J. Norgett,
M. Robinson, and I. Torrens, AERE, Harwell, Rep. TR-494 (1973).
10.
E. Bloom and J. Stiegler, ORNL-4480, 76 (1969).
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
11.
T. Claidson, R. Barker, and R. Fish, Nucl. Appl. and Techn., 9, 10
(1970).
12.
C. Cox and F. Homan, ibid., p. 317.
13.
H. Brager et al., Metal Trans., 2, 1893 (1971).
14.
M. Burger, G. Clottes, and I. Leelere, Franco-Soviet Symposium, Paper No. 12, Obninsk (1972).
15.
K. Bagley, I. Bramman, and G. Cawthorne, in: Proc. Europ. Conf. on Voids Formed by Irradiation
of Reactor Materials, Harwell, BNES (1971), p. 29.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
THE ADSORPTION OF KRYPTON AND XENON
AT LOW PARTIAL PRESSURES ON INDUSTRIAL
SAMPLES OF ACTIVATED CARBON
I. E. Nakhutin, D. V. Ochkin, UDC 541.183:661.879
S. A. Tret'yak, and A. N. Dekalova
At atomic power stations abroad [1] and in the Soviet Union [2], radiochromatographic systems are
used for the purification of off-gas from radioactive contaminants. The main unit of this system is the
adsorber, packed with activated carbon, through which the gas flow with the radioactive contaminants is
passed. As a result of dynamic adsorption and radioactive decay in the adsorber, a stationary state is
established, where the concentration of radioactive gas diminishes toward the outlet of the adsorber t3,41.
The efficiency of radiochromatographic gas purification equipment depends on the adsorptive capacity of
the activated carbon for the inert gases krypton and xenon.
In [5] measurements of the equilibrium adsorption coefficients of krypton and xenon on various grades
of activated carbon over a wide temperature range were reported; it was found that one of the best sor-
bents was SKT carbon [6].
. In the present work we measured the equilibrium adsorption coefficients of krypton and xenon from
air and helium on nine grades of activated carbon manufactured in the USSR over the temperature range
from +20?C to -80?C.
Distribution of the inert gases between the gas phase and the adsorbent was measured in a sealed
circulation apparatus by the method of radioactive tracers according to the concentration of the radioactive
isotopes 85Kr and 133Xe. The adsorption of the carrier gas was measured by a gravimetric method with a
quartz spiral spring balance. Figure 1 shows the temperature dependence of the adsorption coefficient (I')
of xenon from helium (continuous lines) and from air (broken lines) on four grades of activated carbon.
For helium the dependence. of ln(r/T) on 1/T is linear. Gravimetric measurements revealed that the ad-
sorption of helium on activated carbon was insignificant. The calculated values for the differential heat of
adsorption of xenon are given in Table 1 (column 3).
TABLE 1. Properties of the Activated Carbons
Grade of
activated
carbon
Micropore
volume
(Dubinin
method,
cm'/g
Apparent
demity of
the sam-
ple. g/cm'
Heat of ad-
sorption of
xenon from
helium.
kcal/mole
Specific sur
face azea by
the BET
method'
m'/g
SKT
0,457
1,09.103
0,47
SKT-1A
0,470
1,12.103
0,45
SKT-1B
0,458
1,05.103
0,47
SKT-2A
0,441
8,2
1,17.103
0,49
SKT-2B
0,498
7,4
1,04.103
0,44
SKT-3
0,472
7,3
1,10.103
0,47
SKT-4A
0,418
1,33.108
0,55
SKT-6A
0,388
7,5
1,50.103
0,66
ART-2
0,428
1,13.103
0,49
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 295-298, April, 1976. Original article
submitted June 12, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication maybe reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
3 4
Fig. 1. Temperature dependence of the reduced adsorption coefficient of xenon from
(a) helium and (b) air on activated carbons of grades: 0) SKT-2B; ?) SKT-3; ^)
SKT-2A; ^)SKT-6A.
Fig. 2. Temperature dependence of the reduced adsorption coefficient of (a) xenon
and (b) krypton from air on activated carbons of grades: v) SKT-2B; 0) SKT-3; A)
SKT-1A; +) SKT-1B; C)) ART-2; ^) SKT-2A; ?) SET; X) SKT-4A; U) SKT-6A.
Figure 1 shows that the gradient of the straight line varies slightly for various grades of activated
carbon. The heat of adsorption also varies correspondingly. However, our values essentially exceed the
heat of liquefaction of xenon (3.3 kcal/mole [7]). It is probable that these large values of the heat of ad-
sorption of xenon on activated carbon correspond to low filling of the adsorption volume. Even at a tem-
perature of -80?C the maximum quantity of adsorbed xenon in our experiments was no more than 3.8.10-3
neutrons , cm3/cm3 of carbon.
Figure 2 shows the temperature dependence of the adsorption coefficient of xenon and krypton from
air on various grades of activated carbon. For air this dependence is not described by a straight line.
This arises because at a different temperature a different quantity of air is adsorbed on activated carbon;
this reduces the adsorptive capacity for the inert gases. Figure 3 shows the temperature dependence of
the quantity of air that is adsorbed on activated carbon.
We know from [8] that the adsorption isotherms of krypton and xenon on carbonaceous adsorbents
have a form similar to the Langmuir isotherm. For these, the isotherm is characterized by a steep rise
with constant gradient in the low-pressure region; according to the data of [9], the linearity of the iso-
therm is maintained for krypton and xenon up to pressures of 4.10-2 mm Hg.
In the adsorption of krypton and xenon from a mixture the presence of the gas macrocomponent can
alter the shape of the isotherm. This especially applies to air, the adsorption of which has an appreciable
value, as Fig. 3 indicates, unlike helium, which is virtually not adsorbed in this temperature range. For
this reason we measured the initial section of the adsorption isotherm of xenon from a mixture with air
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
Fig. 4. Adsorption coefficient of
xenon from air on activated carbon
of grade SKT-2B as a function of par-
tial pressure at o) 191?K and A)
294?K.
Fig. 3. Adsorption isobar of
air on activated carbons of
grades: 0) SKT-2B; ?)
.SKT-3; A) SKT-1A; +) SKT-
1B; U) ART-2; ^) SKT-2A;
V) SKT; X) SKT-4A; ^)
SKT-6A. X is the quantity of
air adsorbed on unit volume
of activated carbon, 102
g/cm3.
(740 mm Hg) on SKT-2B activated carbon at two temperatures.
Figure 4 presents the adsorption coefficient as a function of
the partial pressure of xenon. At 191?K we observed a small
reduction in the adsorption coefficient as the partial pressure
of xenon increased, but for practical purposes this can be ig-
nored.
When selecting an adsorbent it is not always possible to
measure its adsorptive capacity for a particular substance.
Usually to compare adsorbents more general properties are
used (specific surface area, micropore and transitional pore
volume, pore size distribution), which are measured by stan-
dard methods, using standard substances, in particular nitro-
gen.
In the present work we measured the adsorption iso-
therms of nitrogen at its boiling point on all the samples of
activated carbon, and from these results we calculated the
specific surface area by the BET method [8] and the micropore volume by Dubinin's method [7] (see Table
1, columns 4 and 5).
We calculated the specific surface area by the BET method assuming monomolecular filling of the
energetically uniform surface. Starting from this we could expect to observe a proportional relationship
between the values of specific surface area and the adsorption for different substances. However, we did
not observe this correlation (see Table 1, and Figs. 1 and 2) with the samples of activated carbon in our
experiments, at least in the region of low partial pressures.
In the theory of the volume filling of pores the micropore volume is used as a parameter character-
izing the adsorptive capacity of the adsorbent. As Table 1 shows, the micropore volumes of activated
carbon, measured with nitrogen, and calculated from Dubinin's theory of volume filling [7, 10], also do
not provide a basis for any conclusions on the cause of the adsorption of krypton and xenon at low partial
pressures. Consequently the conventional properties - specific surface area and micropore volume - can-
not be used to estimate the adsorptive capacity of activated carbons for krypton and xenon at low partial
pressures.
It'is of interest to observe that the ranking of carbons by apparent density corresponds to the ranking
by adsorption coefficient. However, we find this rather difficult to explain.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
LITERATURE CITED
1. F. Schumann, Report SZS-133, Berlin, East Germany (1972).
2. E. K. Yakshin et al., At. Energ., 34, No. 4, 285 (1973).
3. I. E. Nakhutin and D. V. Ochkin, Inzh. Fiz. Zh., 9, No. 1, 112 (1965).
4. I. E. Nakhutin, D. V. Ochkin, and Yu. V. Linde, Zh. Fiz. Ehim., 43, No. 7, 1811 (1969).
5. A. M. Trofimov and A. M. Pankov, Radiokhimiya, 7, No. 3, 293 (1965).
6. A. G. Cherepov, B. R. Keier, and T. G. Plachenov, in: Preparation, Structure, and Properties
of Sorbents [in Russian], Vol. 1, Trudy Leningradskogo Tekhnologicheskogo Instituta im. Lensoveta,
Leningrad (1971), p. 39.
7. S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area, and Porosity, Academic Press, New
York- London (1967).
8. S. Brunauer, The Adsorption of Gases and Vapours, Oxford University Press, London (1945).
9. K. Chackett and D. Tuck, Trans. Faraday Soc., 53, No. 12, 1652 (1957).
10. M. M. Dubinin, in: Physical Adsorption from Multicomponent Phases, Proceedings of the 2nd
All-Union Conference on Theoretical Problems of Adsorption [in Russian], Nauka, Moscow (1972),
p. 41.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
TOTAL NEUTRON CROSS SECTION AND NEUTRON
RESONANCE PARAMETERS OF 243AM IN THE
ENERGY RANGE 0.4-35 eV
T.
S.
Belanova, A. G. Kolesov,
V.
A.
Poruchikov, G. A. Timofeev,
S.
M.
Kalebin, V. S. Artamonov,
and
R.
N. Ivanov
One of the main isotopes in the production of, 252Cf is 243Am and it is therefore necessary to know its
neutron cross section with great accuracy. Information about the neutron cross section of 243Am is of
great scientific value in addition to its applied usefulness. It is well known that the data for the total neu-
tron cross section and resonance parameters of this isotope were mainly obtained in 1970-1972. The pres-
ent paper is the result of 243Am transmission measurements by the time-of-flight method which began in
1972 at the SM-2 reactor.
The neutron burst was shaped by a selector with three synchronously revolving rotors suspended in
a magnetic field [1]. A bank of helium counters served as a neutron detector. The measurements were
made with a 4096-channel analyzer. The best resolution of the spectrometer over a 92-m flight path was
70 nsec/m.
Measurements and Results. The target was prepared from a stable dehydrated powder of americium
oxide with a known oxygen content (Am02). To achieve this, the powder was heated inan oxygen atmosphere
Eo, eV
r, meV
28tH, meV
E., eV
r, meV
2grn, meV
0,416?0,003
39?2
0,00084?0,00005 16,56?0,07
27?7
- 0,174?0,005
0,977?0,004
37?2
0,0134?0,0003 17.84?0,07
35?8
0,210?0,007
1,355?0,004
56?1
0,890?0,007 18,14?0,07
27?15
0,046?0,007
1,744?0,005
39?1
0,208?0,002 19,50?0,07
27?10
0,193?0
007
3,134?0,009
47?3
0,012?0,003 19,88?0,07
40?20
,
0,085?0,006
3,424?0,009
45?2
0,253?0,008 20,94?0,07
29?15
0,54?0
18
3,844?0,009
22?5
0,009?0,001 21,09?0,07
16?10
,
0,86?0
22
5,120?0,012
63?2
0,260?0,006 21,85?0,08
27
,
0,14?0,02
6,551?0,015
50?3
0,794?0,044 22,01?0,08
-
7,063?0,017
46?3
0,072?0,011 22,59?0,09
33
1,00?0,60
7,86?0,02
36?9
1,580?0,130 22,72?0,09
19
0,65?0
50
8,39?0,02
40?2
0,010?0,002 24,39?0,09
22
,
0,73?0
02
8,77?0,02
46?2
0,113?0,002 25,38?0,10
40
,
0,14?0,02
9,32?0,02
43?2
0,133?0,002 26,30?0,10
31
0.,06?0,01
10,31?0,03
47?2
0,433?0,007 26,75?0,10
-
1,16?0
03
10,87?0,04
-
0,013?0,002 27,34?0,11
-
,
0,43?0
02
11,27?0,04
49?2
0,267?0,003 28,73?0,12*
-
,
0,97?0
12
11,68?0,05
35?4
0,094?0,002 29.29?0.12*
-
,
0,68?0
15
12,12?0,06
41?3
0,152?0,003 30,12?0,13
-
,
0,49?0
20
12,87?0,06
43?4
2,20?0,20 31,06?0,13*
-
,
0,7?0
15
13,15?0,06
45?5
1,00?0,08 31,49?0,13*
-
,
0,12?0
05
15,12?0,07
33?15
0,070?0,007 32,43?0,14*
-
,
0,88?0
15
15,39?0,07
37?6
0,36?0,08 33,19?0,14*
-
,
1,9?0
2
16,20?0,07
39?3
0,518?0,009 33,92?0,14*
-
,
0,8?0,1
Area method, with
Tj= 30 MeV.
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 298-303, April, 1976. Original article
submitted June 23, 1975; revision submitted August 6, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
b
Fig. 1
for 3 h at 400?C. Following this, 266 mg of powder were poured into an aluminum capsule with a wall
thickness of 1 mm, filling a volume 0.8 X 8.0 x 14.0 mm in size. The target was remotely inserted in the
neutron beam in such a way that transmission could be measured for thicknesses of 0.8 and 14.0 mm,
which correspond to 0.45. 102' and 0.79.1022 atom!cm2. The isotopic composition of the sample was the
following: 243Am, 96.60%; 241Am, 3.32%; 244Cm, 0.08%. The sample contained 79.8% americium.
The statistical accuracy of the measurements was 0.5-1.5% and the neutron background varied from
0.7 to 4.0%. The transmission data were corrected for neutron scattering by oxygen (3% in the thick sam-
ple) and for the contribution of 241Am to the transmission of 243Am. Using resonance parameters obtained
earlier for 241Am [2], the transmission was calculated for the 3.32% content of 241Am in the test sample.
The energy dependence of the transmission T of 243Am after the introduction of the specified corrections
is shown in Fig. 1 for neutrons in the range 0.4-35 eV. Below 26 eV, the resolution of the device made it
possible to calculate neutron resonance parameters by the shape method in accordance with the one-level
Breit - Wigner formula; above 26 eV, the area method was used with the radiation width assumed to be
30 meV. The calculations were performed on a BEM-6 computer [2] with resultant determination of the
resonance position E0, the neutron width 2gFn, and the total width r (Table 1). In addition to statistical
errors, the calculations took into account errors associated with the determination of the shape of the
resolution function and with the distortion of 243Am transmission by the 241Am impurity.
There are two levels at energies of 21.0 and 22.7 eV on the transmission curve. In the process of
fitting the experimental and theoretical transmission curves, it was established that these levels were
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
8,3 8,5
L 25r
16 17
24 26 28 30 32 34 36 E, eV
b
Fig. 1. Transmission of 243Am: -) theoretical calculation by shape method;
experiment; a) to 1 eV, b) 1-8 eV, c) 8-35 eV.
TABLE 2. Values of D and So Obtained for
243A m
so 10-4 I
D, eV
I EO,eV I
Reference
0,84?0,25
1,37
0-15
[7]
0,96?0,10
,0,67?0,06
0-50
[8]
0,89?0,19
0,71?0,10
0,4-35
this work
unresolved doublets. The first level consists of reso-
nances at 20.94 and 21.09 eV, and the second level of
resonances at 22.59 and 22.72 eV. Resonance param-
eters were calculated for all four levels. A similar
situation was pointed out in [3]. The theoretical trans-
mission curve shown in Fig. 1 as the solid curve was
calculated from the neutron resonance parameters.
The agreement of the theoretical and experimental
transmission curves provides evidence for the correct-
ness of the adjustment of 243Am transmission for the
241Am impurity.
The presence of a 20% admixture of inactive elements in the sample made it impossible to determine
the potential scattering cross section op. Such measurements are being made at the present time with a
highly purified sample of 243Am. It should be noted that there is no information about ?p in published data
for this isotope.
Discussion of Results. The values obtained for resonance parameters are basically in agreement
with published data [3-8] although there are cases of considerable divergence of comparable quantities.
The neutron width of the level at 13.15 eV obtained in this work, while agreeing with 2gIn = 0.79
meV [7], is considerably lower than the values 1.33 and 1.45 meV [3, 4]. At 22.59 eV, the neutron width
of 0.52 meV is two times smaller, and at 22.72 eV (2gi'n = 1.33 meV) [3] it is two times greater than the
corresponding neutron widths obtained in the present work for these levels (see Table 1).
We did not confirm the existence of a weak level at 22.011 eV [8], which was obtained with a sample
twice as "thin" as the sample used in this work. The calculated value of the total resonance integral was
I= 1740t150b.
Information about resonance parameters in the energy range 0.4-35 eV made it possible to evaluate
certain statistical properties of the 243Am nucleus. We calculated the average level spacing D = 0.71 f 0.10
eV, the mean reduced neutron width 2gi'n = 0.127 meV, and the strength function So = 0.89 f 0.19 - 10-1.
The integral distribution of reduced neutron widths is given in Fig. 2. Analysis showed [9, 10] that it cor-
responds to a Porter - Thomas distribution with number of degrees of freedom u = 1,01 t 0.24. The best
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 Declassified and Approved For Release 2013/04/10: CIA-RDP1O-02196ROO0700070004-7
0 0,2 0,4 0,6 01
(r,?/2P,?)y2
Fig. 2
I I I I
10 20 30 E, eV
Fig. 3
Fig. 2. Integral distribution of reduced neutron widths for 243Am
(N is number of resonances): -) Porter - Thomas distribution
for one degree of freedom normalized to 55 levels; - - - -)
same distribution normalized to 48 levels; histogram is experi-
mental distribution.
Fig. 3. Sum of reduced neutron widths Z 2grO as a function of neu-
tron energy. The strength function T'O,'D is given by the slope of
the line (So = 0.96.10-4).
agreement of this distribution with the experimental histogram (solid line in Fig. 2) was obtained for a
neutron-level number n = 55 and for 2grO = 0.118 meV. This indicates that one should assume the loss
of seven weak levels below 35 eV. With the inclusion of these levels, D = 0.62 eV and So = 0.95 ?10-4,
which is in good agreement with So determined directly from the experimental data (including also So =
0.96. 10-4 obtained from the slope of the line in Fig. 3). Values of D and So obtained by various authors
are compared in Table 2. 1
The overestimate of the value of b in [7] is explained by the fact that a total of 12 levels was ob-
served in the energy range 0-15 eV. Subsequent measurements showed that there were 21 resonances in
the 243Am nucleus in that energy range [4, 5, 8]. Figure 4 shows the distribution of spacing between neu-
tron levels; the solid curve describes the Wigner distribution for a single system of levels [11] and the
dashed curve is the superposition of two distributions, while the histogram gives the experimental distri-
bution. It is clear from the figure that the Wigner distribution for a single system of levels fits the histo-
gram better despite the fact that two systems of levels should be realized in the 243Am nucleus. If one is
not seeking deeper physical causes for this, * the existing situation may simply be the consequence of in-
sufficient resolution of closely located levels or loss of weak resonances.
The experimental data were analyzed for long-range correlation in accordance with the A3 test for
an orthogonal ensemble proposed by Dyson and Mehta [12]. An experimental value A3 = 0.54 was deter-
mined and theoretical values A3 = 0.77 f 0.22 for two systems of levels and A3 = 0.39 ? 0.11 for a single
system of levels. The agreement between experimental and theoretical values of A3 verifies the correct-
ness of the Dyson- Mehta theory if a single system of levels is realized in the nucleus. In the present
case, a comparison of the values of ,\3 does not permit one to arrive at any conclusion whatever about the
levels in the 243Am nucleus.
Figure 5 shows the results of the a(K) test - the correlation of the position of two levels between
which there are K levels.
The authors are grateful to Yu. S. Zamyatnin and Yu. G. Abov for interest in the work and valuable
*It has been suggested [13] that there is a "repulsion" of levels with different spin values.
E2grn
6
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
Nd D
50
06 1,2 1,8 2,4 40 . DID
Fig. 4. Fig. 5.
Fig. 4. Distribution of spacing between levels in IA3Am
(N, number of resonances; D, spacing between them).
Fig. 5. - Correlation c (K) of positions of two levels be-
tween which there are K levels for 243Am: UW, DE)
theoretical values of a(K) for uncorrelated Wigner distri-
bution and for an orthogonal ensemble; ?) experiment;
- - - -) limits of statistical spread of v (K) for 50
levels.
discussions, and also to V. A. Safonov, S. I. Babin, S. N. Nikol'skii, T. V. Denisova, V. Ya. Gabeskir-
iya, V. M. Nikolaev, and G. V. Kuznetsov, who provided assistance in various stages of the work.
1. S.. M. Kalebin et al., Proceedings Neutron Physics Conference [in Russian], Pt. II, Naukova
Dumka, Kiev (1972), p. 267. _
2. T. S. Belanova et al., At. Energ., 38, No. 1, 29 (1975).
3. O. Simpson et al., Report ANCR-1060 (1972).
4. J. Berreth et al., Rep. IN-1407, USAEC (1970), p. 66.
5. O. Simpson et al., Bull. Amer. Phys. Soc., 15, 569 (1970).
6. O. Simpson et al., Rep. IN-1407, USAEC (1970), p. 72; Nucl. Sci. Engng., 55,273 (1974).
7. R. Cote et al., Phys. Rev., 114, 505 (1959).
8. BNL-325, Third Ed. (1973).
9. C. Porter and R. Thomas, Phys. Rev., 104, 483 (1956).
10. H. Sharma and Ray. Ram, Progr. Theor. Phys., 51, 1642 (1974).
11. L. Lynn, The Theory of Neutron Resonance Reactions, Clarendon Press, Oxford (1968).
12. F. Dyson and M. Mehta, J. Mathem. Phys., 4, 701 (1963).
13. E. Wigner, in: Statistical Properties of Nuclei, J. Garg (editor), New York- London (1972), p. 7.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
TOTAL NEUTRON CROSS SECTION AND NEUTRON
RESONANCE PARAMETERS OF 241AM IN THE
ENERGY RANGE 0.004-30 eV
S.
M.
Kalebin, V. S. Artamonov,
R.
N.
Ivanov, G. V. Pukolaine,
T.
S.
Belanova, A. G. Kolesov,
and
V.
A. Safonov '
The energy dependence of the total neutron cross section (rt of 241Am was investigated in the energy
range up to 8 eV by the time-of-flight method at the heavy-water reactor of the Institute of Theoretical and
Experimental Physics. The best resolution of the spectrometer was 14 nsec/m [1]. Similar studies were
made at the SM-2 reactor at NIIAR [2] for neutron energies of 8 eV and above. The measurements were
made with identical neutron selectors and detectors [1, 3]. In both experiments, the same sample with
thicknesses of 0.63 ?1021 and 3.3 ?1021 atom/cm2 was used which contained 99.99% of the isotope 241Am.
The experimental conditions and the procedure for analysis of the experimental data were identical at both
reactors [2].
Results of Measurements. The energy dependence of the total neutron cross section is shown in Fig.
1. Figure 2 shows the dependence of the experimentally obtained transmission T on neutron energy. The
high purity of the americium sample and its monoisotopic composition made it possible to assert that all
13 levels observed in the energy range 0.004-8 eV belong to the nucleus 241Am. The spectrometer resolu-
tion made it possible to calculate the parameters for these resonances by the shape method in accordance
with the one-level Breit - Wigner formula. The resultant parameters were used to calculate a theoretical
transmission curve which is shown in Fig. 2 as a solid curve. A negative level at 0.425 eV was introduced
in order to match the theoretical value of T with the experimental value in the thermal energy region (see Fig. 2).
TABLE 1. Neutron Resonance Parameters for 241Am
Eo, eV
r, meV
2grn. meV I
I Eo, eV
r, meV
2grn, meV
-0,425
40
2gF, =1,0
14,66?0,07
44?5
2,30?0,13
0,306?0,002
45?1
0,0556?0,0004
15,66?0,07
32?12
0,215?0,012
0,573?0,004
43?1
0,0928?0,0016
16,35?0,07
44?5
1,185?0,033
1,268?0,004
41?2
0,330?0,016
16,81?0,07
31?8
0,575?0,020
1,916?0,005
46?2
0,107?0,002
17,69?0,07
40?10
0,373?0,016
2,538?0,008
41?2
0,070?0,001
18,09?0,07
-
-
2,581?0,009
38?2
0,150?0,004
19,39?0,07
37?12
0,182?0,016
3,956?0,009
28?3
0,230?0,008
20,28?0,07
-
0,050?0,010
4,947?0,010
31?5
0,176?0,005
20,84?0,08
-
0,064?0,011
5,390?0,012
38?7
0,844?0,114
21,72?0,08
-
0,067?0,012
6,100?0,013
42?14
0,116?0,005
22,74?0,09
-
0,070?0,012
6,650?0,015
-
0,05?0,03
23,08?0,09
-
0,39?0,05
7,53?0,02
-
0,07?0,04
23,33?0,09
-
0,40?0,05
8,17?0,02
42?5
0,096?0,004
24,17?0,09
-
1,27?0,08
9,11?0,02
48?3
0,358?0,006
25,05?0,10
-
-
9,84?0,03
48?3
0,370?0,007
25,60?0,10
-
1,21?0,08
10,11?0,03
-
0,025?0,004
26,50?0,10
-
-
10,39?0,03
45?4
0,294?0,007
26,67?0,10
-
-
10,99?0,04
52?4
0,382?0,008
27,52?0,10
-
-
11,58?0,05
-
0,018?0,003
27,65?0,10
-
-
12,06?0,06
-
0,007?0,003
28,31?0,11
-
0,40
12,86?0,06
44?5
0,116.?0,009
28,82?0,12
-
0,35
13,80?0,06
-
0,050?0,015
29,43?0,12
-
0,61
14,32?0,06
-
0,066?0,012
Translated from Atomnaya Energiya, Vol, 40, No. 4, pp. 303-307, April, 1976. Original article
submitted June 25, 1975; revision submitted August 6, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
-V VIIH fill jillif
till IRII #111!
2 4 6 E, eV
Fig. 1. Total neutron cross section of 241Am from 0.004 to 8 eV;
?) experimental points; -) theoretical curve obtained from the
resonance parameters in Table 1 with the.inclusion of a negative
level at E = 0.425 eV; - - - -) without inclusion of the- negative
level at 0.425 eV.
i 1 i I -L -I
0,02 qG4 0,06 0,08 0,1
I
02
i i i i i i i
04, 0,6 48 1,0 E, eV
2,0 2,5 3r0 4,0 50 4,0 7,0 E,eV
Fig. 2. Transmission of 241Am in the range 0.004-8 eV: ?) experiment;
and - - - -) theoretical calculations by the shape method respectively with and
without the negative level at 0.425 eV.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
g4 q6 48
(GO/217) 112
Fig. 3 Fig. 4
Fig. 3. Integral distribution of reduced neutron widths in 241Am (N, number
of resonances): -) Porter -Thomas distribution for a single degree of
freedom normalized to 44 resonances; - - - -) the same distribution nor-
malized to 38 resonances; histogram is experimental distribution.
Fig. 4. Sum of reduced neutron widths E 2grn as a function of neutron
energy. The strength function To IT) is given by the slope of the line (So =
0.86.10-4).
0,6 1,2 1,8 2,4 3,0 DID
Fig. 5. Distribution of
spacing between levels in
241Am (N, number of re-
sonances; D, spacing
between them).
Table 1 gives the level position E0, the values of the neutron width
2grn, and the total width r for 45 resonances, including resonances mea-
sured previously by the authors [2]. Two levels at 2.538 and 6.6b eV were
found for the first time in 241Am.
Discussion of Results. The values of the resonance parameters
given in Table 1 basically agree with other published data [4-9]. We point
out the discrepancies.
1. A level at 1.68 eV was obtained in a study of fission of the nucleus
241Am [4, 5]; data on resonance parameters for it were not presented. This
level was found neither in the present work nor in other studies of the total
neutron cross section of 241Am [4, 6, 7].
2. Levels at 2.36 and 4.40 eV with respective neutron widths of 0.080
and 0.027 meV were given in [4, 6]. We failed to observe these levels in
the present work although resonances with narrower neutron widths were
recorded.
3. Strong levels at 6.78 and 7.97 eV with neutron widths of 0.23 and 0.79 meV respectively [4, 7]
were also not observed. Judging from the values of 2g]Fn, these levels should appear considerably more
clearly than neighboring levels which were observed (see Table 1).
4. With respect to the previously published data [2], one should add that only a single level was
found at 15.66 ? 0.07 eV with 2grn = 0.215 meV where, according to the data in [7], two very close levels
were resolved at 15.60 t 0.05 and 15.73 f 0.05 eV having the respective neutron widths 0.16 f 0.10 and
0.17 ? 0.10 meV. However, only a single resonance at 15.8 eV with 2grn = 0.40 meV was observed in this
energy range in [6]. Analysis of the neutron width of the level at 15.66 eV does not permit consideration
of it as a double level with the parameters specified in [7].
5. The existence of a resonance at 16.02 eV, which has the high value 2gl'n = 0.14 meV [7] and
therefore should have been noted in [2], was not confirmed.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
Fig. 6. Correlation
v(K) of the positions of
two levels between
which there are K levels
in 241Am: UW, OE)
theoretical values of
9(K) for uncorrelated
Wigner distribution
and. orthogonal ensemble;
?) experiment; - - - )
limit of statistical
spread of a (K) for 30
levels..
What has been said above indicates that levels at the energies 2.36,
4.40, 6.78, 7.97, and 16.02 eV were erroneously assigned to the nucleus
241Am. A capture cross section 6c = 624 f 20 b and a total cross section
at = 640 f 20 b were measured at the thermal point. In addition, a total
resonance integral I = 1650 f 120 b was calculated, which is in good agree-
ment with the value I = 1498 f 120 b [4].
Information about the resonance parameters of 241Am in the energy
range 0.025-26 eV made it possible to evaluate certain statistical properties
of this nucleus. We calculated the average level spacing b = 0.67 f 0.10 eV,
the average reduced neutron width 2grn = 0.102 me V, and the strength func-
tion So = (0.76 f 0.18). 10-4. The integral distribution of the reduced neutron
widths is shown in Fig. 3. Analysis of the distribution [10,11 ] showed that it
corresponded to a Porter - Thomas distribution with number of degrees of
freedom v = 1.07 * 0.23. Best agreement of this distribution with the experi-
mental histogram (solid line in Fig. 3) was obtained for a neutron-level num-
ber n = 44 and 2g7Pn = 0.096 meV. This indicates that one should assume the
loss of six weak levels below 26 eV. With these resonances included, D =
0.6 eV and So = 0.80 ?10-4, which is in good agreement with So determined
directly from experimental data (including also So = 0.86.10-4 obtained from
the slope of the line in Fig. 4).
The distribution of spacing between neutron levels is shown in Fig. 5.
The solid curve represents the Wigner distribution for a single level system,
the. dashed curve, the. superposition of two systems .of levels [12], and the
histogram the experimental distribution. It is clear from the figure that the
Wigner distribution for a single system of levels better describes the histo-
gram despite the fact that two systems of levels should be realized in 241Am.
If one is not seeking deeper physical reasons, * this situation may simply be the consequence of insufficient
resolution of closely lying levels or of loss of weak resonances, particular evidence of which is the Porter
- Thomas distribution obtained.
The experimental data was analyzed for long-range correlation in accordance with the A3 test for an
orthogonal ensemble proposed by Dyson and Mehta [13]. We obtained the experimental value A3 = 0.367
and the theoretical values A3 = 0.723 ? 0.219 for two systems of levels and A3 = 0.362 t 0.110 for a single
system of levels. Agreement of experimental and theoretical values of A3 confirms the correctness of the
Dyson- Mehta theory for the case where one system of levels is realized in a nucleus.
Figure 6 presents the results of the (T(K) test - correlation of the positions of two levels between
which K levels are located.
The authors are grateful to Yu. G. Abov and Yu. S. Zamyatin for interest in the work and also to
T. V. Denisova and V. A. Poruchikov who assisted in the calculations.
LITERATURE CITED
1. S. M. Kalebin et al., Yad. Fiz., 14, 22 (1971).
2. T. S. Belanova et al., At. Energ., 38, No. 1, 29 (1975).
3. S. M. Kalebin et al., in: Proceedings Neutron Physics Conference [in Russian], Pt. II, Naukova
Dumka, Kiev (1972), p. 267.
4. BNL-325, 3rd edition (1973).
5. C. Bowman et al., Phys. Rev., 137, 326 (1965).
6. R. Block, L. Slaughter, and J. Hervey, ORNL-2718 (1959), p. 26.
7. G. Slaughter, J. Hervey, and R. Block,. ORNL-3085 (1961), p. 42.
8. H. Derrien, in: Proceedings Neutron Physics Conference [in Russian], Pt II, Izd. ONTI FEI,
Obninsk (1974), p. 246.
9. B. Leonard and E. Seppi, Bull. Amer. Phys. Soc., 4, 31 (1959).
10. C. Porter and R. Thomas, Phys. Rev., 104, 483 (1956).
11. H. Sharma and Ray. Ram, Prog. Theor. Phys., 51, 1642 (1974).
*It has been suggested [14] that there is a "repulsion" of levels with different values of spin.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
12. L. Lynn, The Theory of Neutron Resonance Reactions, Clarendon Press, Oxford (1968).
13. F. Dyson and M. Mehta, J. Mathem. Phys., 4, 701 (1963).
14. E. Wigner, in: Statistical Properties of Nuclei, J. Garg (editor), New York-London (1972), p. 7.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
Yu.
G.
Bamburov,
S.
B.
Vasserman,
V.
M.
Dolgushin,
V.
F.
Kutsenko,
N.
G.
Khavin, and
B.
I.
Yastreva
The ELIT-1B electron accelerator (Fig. 1) is one of the pulsed high-voltage accelerators which were
developed in the last few years by*the Institute of Nuclear Physics of the Siberian Branch of the Academy of
Sciences of the USSR and which make use of a tesla transformer [1]. The ELIT-1 accelerator [2], which
was built in 1966 in the Institute, was the prototype.
When compared with the ELIT-1, the basic dimensions of the accelerator were maintained yet all the
basic parameters of the ELIT-1B (electron energy, pulse current, average current, and average power)
were substantially increased by improving the design of the apparatus, the electrical supply system, the
vacuum system, etc. This affects mainly the average power which was increased by one order of magni-
tude.
Particular attention was paid to the problems related to the reliability which, in turn, is dictated by
the requirements to be fulfilled by industrial accelerators. It was found by long-term testing that the cru-
cial components of the accelerator, viz., the high-voltage winding of the transformer and the accelerating
tube, work at least 1000 h without defects. The service life of the cathode of the electron gun was 400-500
The combination of high pulse power and high average power of the electron beam, the compactness
of the accelerator, the simplicity of its design, and its reliable operation make it possible to use the ELIT-
1B accelerator for various industrial applications. The international conference which was held in April
1974 in Vienna and which was concerned with the sterilization of medical materials by irradiation [3] and,
in addition, the achievements of various organizations irradiating medical materials, which were exhibited
as documents on the stand of the Institute of Nuclear Physics, have shown that this accelerator is very
promising for the sterilization of medical materials by an electron beam.
The basic parameters of the accelerator are as follows: accelerated electron energy up to 1.4 MeV;
pulse current up to 50 A; pulse power up to 60 MW; pulse duration between 30 nsec and 2.5 ?sec; and
Fig. 1. The ELIT-1B accelerator.
pulse repetition frequency up to 100 Hz. During long-
term operation, the average beam current can reach
4.5 mA; in forced operation, the beam current can be
increased to 6.5 mA. The beam parameters can be
adjusted within wide limits. The accelerator was
tested under various conditions, among them long-
term operation (1000 h) at an electron energy of 1.1-
1.2 MeV, a pulse repetition frequency of 100 Hz, and
an average beam power of 4-5 kW.
The Electrical Circuit. Figure 2 shows a sim-
plified scheme of the accelerator. The primary cir-
cuit (L1C1) and the secondary circuit (L2C2) of the tesla
transformer have a resonance frequency of 60 kHz and
a coupling coefficient of almost 0.6 at which the maxi-
mum voltage in the secondary circuit is reached during
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 308-311, April, 1976. Original article
submitted May 26, 1975; revision submitted October 6, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication maybe reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
Fig. 2. Structural electrical scheme: 1) voltage regula-
tor; 2) rectifier; 3) choke; 4) commutator; 5) control
block of the electron gun; 6) grid of the gun; 7) supply
block of the focusing lens; 8) beam-sweeping system; 9)
measurement circuits and circuit for the protection from
subsequent breakdowns; 10) supply block of the gun.
the second half-wave of the oscillations. The capacitor C1 (1.1 ?F) is charged to 15-25 kV. The capacitor-
charging process is oscillatory. The charging apparatus comprises an RNTT 330-250 voltage regulator
with thyristors, an industrial power transformer with a rectifier, and a charging choke. The oscillations
which begin in the circuits when the thyratron section of the commutator is closed are terminated by the
full discharge of the capacitor C1. The forward branch of the commutator consists of two TGI1-2500/35
thyratrons connected in parallel; VCh-160 diodes (40 of them connected in series) are used in backward
direction. A load resistor RL is inserted into the diode branch of the commutator. Since energy is trans-
ferred into the secondary circuit mainly when the forward branch of the comutator is effective, the load
resistor hardly influences the efficiency with which energy is transferred from-the primary circuit to the
secondary circuit. The strong attenuation which the load resistor causes liberates the circuit from exces-
sive heating and improves the breakdown strength of the high-voltage circuit. For the value of the load re-
sistor, which was used in the commutator and which is equal to the characteristic resistance of the cir-
cuits, the amplitude of the second half-wave (which is in-phase with the accelerating half-wave) of the vol-
tage U2 amounts to about 50%Io of the first half-wave. The load resistor is built of nickel- chromium wire
applied as a bifilar winding on an insulating body; the resistor is cooled with running tap water.
The dissipation of the energy, which was not used for accelerating electrons, by the load resistor
reduces the efficiency of the apparatus when compared with the recuperation conditions of [2] but preserves
the other advantages of recuperation (small energy losses inside the accelerator and short duration of the
high-voltage effect). The commutator can be easily adjusted and works reliably. The progress which in-
dustry has made in the field of powerful controllable gas-discharge tubes and semiconductor diodes makes
it possible to plan the future development of reliable commutators with energy recuperation for accelera-
tors of the type under consideration.
The control block of the electron gun is mounted inside the high-voltage electrode and has its poten-
tial. This control block provides for the heating of the gun and shapes the control pulse which is applied
to the grid and has an amplitude of up to 5 kV. The pulse generator is triggered by a fraction of the high
voltage, which is derived from a capacitive transducer. In order to obtain the optimum position of the
control pulse on the time scale and in relation to the accelerating voltage under the various conditions of
operation, the trigger pulse is passed through an adjustable delay line. The delay of the line is changed
by a switch (step selector switch) which is operated by application of light pulses to the light guide shown
in Fig. 3. The same switch changes the delay of a line with which the duration of the control pulses is
adjusted. The corresponding light signals are introduced into the block via a second light guide.
A focusing lens and a beam-sweeping system are mounted in the exit section of the accelerator. The
focusing lens is applied by a sinusoidal current pulse having an amplitude of up to 80 A and a duration of
100 p sec. The beam passes in succession through 32 positions on the foil of the exit horn. This sweep is
obtained by applying current pulses with a variable amplitude to the deflecting coils mounted on the outside
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
01050 of the exit horn: Since the deflecting pulse is much
longer than the pulses of the electron current (4 msec
and 1.5 psec), the field generated by the deflecting coils
is quasi-constant. The independent amplitude adjust-
ment of the deflecting pulses makes it possible to adjust
the current distribution in the exit window so that either
a uniform current density distribution over the length of
the window or a current density distribution following a
certain law is obtained. When the pulse repetition fre-
quency is changed, the sequence of the beam positions on
the foil remains unchanged.
Fig. 3. Design of the accelerator: 1)
shielding electrode; 2) capacitive sensor; 3)
gun-control block; 4) electron gun; 5) tank;
6) high-voltage electrode; 7) electrode; 8)
primary coil; 9) tubes for cooling the pri-
mary coil; 10) secondary coil; 11) accel-
erating tube; 12) valve; 13) nitrogen trap;
down events which could damage the accelerating tube,
the secondary coil, and other components, a protection
is provided. The protection circuit removes the pulses
triggering the commutator after a first breakdown and
de-energizes the circuit charging the capacitor C1. The
short front appearing on the accelerating voltage at the
time of the breakdown is the signal for triggering the
above circuit. The short front is derived from the cap-
acitive divider C31 C41 which at the same time serves
for measuring the high voltage.
The operation of the deflecting system, the focus-
ing lens, and the commutator is synchronized by a gen-
erator of delayed pulses. The main components of the
supply source are mounted in two cabinets with the di-
mensions 1.8 x 0.8 x 0.9 in and in two racks (power rack
and control rack) with the dimensions 1.9 x 0.6 x 0.5 in.
14) NORD-250 vacuum pump; 15) titanium Construction of the Accelerator. The high-voltage
foil; 16) exit horn; 17) sweep system: 18) transformer, the accelerating tube, and the control
Rogowski loop; 19) nitrogen trap; 20) focusing block of the gun are mounted in a tank filled with an
lens; 21) vacuum volume; 22) light guide (2 inert gas (SF6) under a pressure of 10 atm (see Fig. 3).
of them).
The turns of the primary coil, which is made of
copper tubing, are cooled with water. The secondary
coil is electrically a single-layer coil; a second layer is required for transferring the supply voltage over
two parallel leads to the control block of the electron gun. The coil is wound on a body of organic glass
(Plexiglas). In order to reduce overvoltages between the turns of the coil in the case of electrical break-
down of the entire voltage, a protective electrode is provided. The accelerating tube is subdivided into
sections. The insulating rings are made of Plexiglas. The insulator surface facing the vacuum is cor-
rugated. The average electrical field strength amounts to 25 kV/cm on the insulator.
In the center of the tube, the electrodes are drawn together to face each other. The electrical field
strength in the upper part of the tube reaches 100 kV/cm. The cathode of the gun is made of lanthanum
hexaboride (LaB6). The cathode has a diameter of 17 mm. An NORD-250 magnetic discharge pump with
nitrogen traps is used for evacuating the accelerator tube. During operation, the vacuum in the lower part
of the tube is 10-8 mm Hg.
The horn of the exit section has a window with a size of 40 x 6 cm made of 100-p-thick titanium foil.
The beam diameter on the foil is adjusted by a pulsed magnetic lens.
The accelerator and the exit section have a weight of 1 ton. The tank has a diameter of 0.9 in and a
height of 0.85 m.
Modes of Accelerator Operation and Results of Tests. Two modes of accelerator operation are pro-
vided. In the first mode, the parameters can be varied to a very large extent, particularly as far as the
pulse duration of the beam current is concerned, which can be adjusted from a panel to 30, 70, 100, 130,
160, 200, 240, 300, 500, and 1000 nsec with flanks of about 10 nsec. In the second mode of operation,
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
which is designated mainly for long-term operation with a high average power, the pulse duration is fixed
and equal to 2.5 ?sec. This mode of operation also allows the adjustment of the other parameters (except
for the pulse duration). The nonmonochromaticity (the total energy spread) of the beam amounts in this
case to 15%. In both modes of operation, the electron energy can be adjusted from 0.4 to 1.4 MeV, the
pulse current can be adjusted from 0 to 50 A, and the frequency of the pulse repetition can be changed
from single pulses to 100 Hz. The current pulses are rectangular in both modes of operation and for all
pulse durations.' The transition from one mode of operation to the other makes it necessary to exchange
the control block of the electron gun inside the tank of the accelerator (see Fig. 1).
As indicated above, long-term tests of the accelerator were made at an average beam power of 4-5
kW. At a beam power of 5 kW and a beam energy of 1.2 MeV, electrical breakdown occurs in the tube on
the average every 3-5 h of continuous operation. After that, the protective means shut off the high voltage.
The accelerator is ready to be put into operation again 1-2 min later. These breakdowns do not result in
irreversible changes in the accelerator. At a beam power of 4 kW and a beam energy of 1.1 MeV, there
are practically no breakdown events. The average beam power can be increased to 7 kV for short time
intervals (by increasing the current). The accelerator can be operated in this mode for 10 min without
switching it off. The temperatures of the tube sections and of the secondary coil were monitored during
long-term tests with an average beam power of 5 kW. The readings of temperature indicators working
with the fusion principle did not exceed 55?C.
We indicate below the dependence of the maximum pulse current and of the accelerator power upon
the electron energy at a pulse repetition frequency of 1-2 Hz and a pulse duration of 2.5 ?sec:
E,
MeV
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
I,
A
38
42
48
54
56
50
40
20
P,
MW
27.5
33.5
43
54
61
60
52
28
The maximum current is given by the capacity of the electron gun; when the electron energy is re-
duced, the current amplitude is given by the transmissivity of the tube channel; at high energies, the cur-
rent is limited by the electrical breakdown strength of the tube.
We also tested a modification of the accelerator with an electron gun of greater power (cathode dia-
meter 30 mm) and a slightly modified configuration of the electrodes in the accelerating tube. We obtained
with this version a pulse current of 150 A at an energy of 1.2 MeV, a pulse duration of 2 nsec, and a pulse
repetition rate of up to 50 Hz.
1.
S. B. Vasserman et al., The Pulsed High-Voltage Electron Accelerators of the Institute of Nuclear
Physics (Novosibirsk) for Industrial Applications and Experiments, 4th All-Union Conference on
Accelerators of Charged Particles [in Russian], Moscow (1974).
2.
E. A. Abramyan and S. B. Vasserman, At. Energ., 23, No. 1, 44
(1967).
3.
Proc. Intern. Conf. "Sterilization by Ionizing Radiation," Vienna, April 1-4 (1974).
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
CROSS SECTIONS OF THE INTERACTION OF
PROTONS AND ELECTRONS WITH ATOMS OF
HYDROGEN, CARBON, NITROGEN, AND OXYGEN
When one wishes to obtain the statistical distribution functions of the radiation energy absorbed by
the sensory volumes of biological objects with a size of -10-100 A, it is convenient to employ calculation
methods in which both the differential and the total cross sections of the interaction of heavy charged par-
ticles and electrons with the atoms of the biological tissue are used. The information on the required
cross sections of interaction is far from being complete in the published literature. The goal of the pre-
sent work is to supply some of the missing information and to collect and analyze literature data.
We consider for heavy particles the energy range in which only ionization and excitation of the atoms
of the medium are the important processes. For example, this energy range of the protons begins at 200
keV [1]. In the case of electrons, we consider ionization, excitation, and elastic scattering from the
energy 100 eV.
Data on the cross sections of the excitation of atoms by charged particles have been compiled in [2-4].
However, the calculations were made only for some, transitions and the results serve to verify the applica-
bility of various approximations in the quantum mechanical theory. Using these approximations frequently
implies considerable computational work which at times does not justify the effort. Therefore, the first
Born approximation as the simplest approximation. was used to obtain systematic data on the cross section
of excitation of the most intensive transitions in light atoms excited by charged particles. The concept of a
generalized oscillator strength of the transitions can be used in this approximation for both resolved and
forbidden transitions. The single-electron approximation was used in [5] to calculate the generalized os-
cillator strength of several atoms ranging from helium to sodium. When the usual expression for the tran-
sition probabilities in the Born approximation is used [6], the following formula for the excitation cross
section is obtained:
4k2
4na2 dK2
6Un EAE f Own (Kz) gz
n k2(AEn/2E)2
where go-- n denotes the cross section of the excitation of a transition, cm2; ao denotes the radius of the
first Born orbit, cm; E denotes the energy of the incoming particle, Rydberg units; DEn denotes the
energy of the excitation of the transition, Rydberg units; k denotes the wave number of the incoming par-
ticle, a.u.; K denotes the momentum transferred from the incoming particle to the atom, a.u.; and fo-n
denotes the generalized oscillator strength of the transition.
TABLE 1. Energy (eV) of the Transitions of Highest Intensity
Transition
Atom
2S-2P
I 2P-3S
I 2P-4S
I 2P-5S
I 2P-3P I 2P-4P I 2P-5P
2P-3d
2P-4d
C
13,12
7,48
9,68
-
8,84
10,08
10,53
9,83
10,43
N
10,93
10,3
12,9
10,6
12,0
13,3
-
13,0
13,7
0
15,65
9,52
11,9
12,7
11,0
12,4
-
12,1
12,76
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 311-317, April, 1976. Original article
submitted June 9, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication maybe reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
4-.
ZL
104 Ep, keV ke,eV Ep, key
Fig. 1 Fig. 2
Fig. 1. Cross sections of the inelastic interactions of protons with atoms of tissue-
equivalent matter: -) cross sections which were calculated for ionization with the
theory of binary collisions; - - -) cross sections of the excitation of transitions of
highest intensity in H, C, N, and 0 atoms; the cross sections were calculated from the
generalized oscillator strengths of the transitions. -
Fig. 2. Cross sections of the interaction of electrons with H, C, N, and 0 atoms:
- - -, and - ? - ? -) cross sections of ionization, elastic scattering, and ex-
citation, respectively.
We have considered these transitions in atoms of carbon, nitrogen, and oxygen, which render the
greatest contribution to the cross section of excitation. The energies of these transitions were taken
from [7] and are listed in Table 1. In the case of electrons, E = Ee/]Ry in Eq. (1); in the case of protons,
E = m/M(Ep/Ry).
When the cross sections of the excitation of hydrogen were calculated, the rigorous formulas were
used in the first Born approximation [6]. After some simple yet laborious transformations of the formulas
for the matrix elements of the transitions, we obtain for the hydrogen atom:
b
4.617.10-11 dx
a IS. 25= E f (9?4x)6 '
a
b
1.039.10-10 dx
Q1S-2P= E J x(9?4x)6
61S-3P= E
(16+9x)8 x
a
b
13?4P= 4.155.10-9 r (768x2 + 928x + 275)2 dx
E J x(25+16x)10
a
a
b
5.259. 10-10 C (16+27x)2 dx
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Fig. 3 Fig. 4
Fig. 3. Angular distributions of the outgoing electrons in ionizing collisons of 1.7 MeV
protons with nitrogen atoms : the cosine of the electron exit angle is platted to the ab-
scissa; the double differential cross section is plotted to the ordinate; -) calcula-
tions based on the theory of binary collisions; the interaction of the proton with the out-
going electron was brought into account; - - -) experimental results of [13].
Fig. 4. Differential ionization cross sections over the transferred energy W of 14N7
atoms; protons of various energies (the calculations were made in an approximation
given' by the theory of binary collisions).
The cross section of excitation is expressed in cm2; E denotes the energy of the electrons or heavy
charged particles and is expressed in Rydberg units [calculated as in Eq. (1)]; a = E(AEn/2E)2; and b =
4E. The energies of the transitions whose excitation cross sections were determined with Eqs. (2)- (5)
are 10.2, 10.2, 12.09, and 12.75 eV, respectively.
The total excitation cross section (Ft of a particular atom is equal to the sum of the partial cross
sections. The average energy of excitation is determined with the formula
AE _ ~j' AE,, ((7p_n/6t)
n
The average excitation energy of the atoms of hydrogen, carbon, nitrogen, and oxygen in the energy inter-
val of the incoming particles under consideration is practically constant and equal to 10.6, 11.8, 11.1, and
13.4 eV, respectively. Figure 1 shows as an example the results of calculations which were made for the
cross sections of excitation of these atoms by protons with energies between 100 keV and 20 MeV. Figure
2 shows the results of calculations of the cross sections of excitation of light atoms by electrons with ener-
gies between 100 eV and 10 keV (dash-dot lines).
TABLE 2. Ionization Potentials, Effective Number of Electrons, and Average Electron
Energies for all Subshells of Carbon, Nitrogen, Oxygen, and Hydrogen Atoms
Jt, eV
Nt
Ei, eV
Atom
Ll I
Ly
I L3
K
L,
Ly I
L3
I K
L,
L.
L3
K
12C6
11,26
16,6
24,96.
307
2
4/3
2/3
2
35,9
37,0
37,0
441,5
14N7
14,54
19,7
33,8
420
3
5/4
3/4
2
42,8
44,0
44,0
610,1
1608
13,6
28,5
40,0
562
4
4/3
2/3
2
70,3
71,9
71,9
8
Ht
-
-
13,6
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U 12
m
/
0,4 46 48 1,0 1,2
e/2me Vp
Fig. 5 Fig. 6
Fig. 5. Comparison of the differential cross sections of the ionization of 14N7 atoms by
protons with the experimental data of [13]; the differential cross sections were calcu-
lated with the theory of binary collisions and in the approximation of scattering at free
electrons. The kinetic energy of the electron emitted in the ionization event is plotted
to the abscissa in units of the maximum energy; -) ratio of the cross sections calcu-
lated with the theory of binary collisions to the experimental cross sections and is
plotted to the ordinate; - - - -) ratio of the classical cross section to the experimen-
tal cross section and is plotted to the ordinate.
Fig. 6. Comparison of the differential cross section of the ionization of nitrogen and hy-
drogen atoms by protons with the energies 1) 0.2, 2) 1.0, and 3) 7.0 MeV; the differen-
tial cross sections were calculated with the theory of binary collisions and with the ap-
proximation of scattering at free electrons (the discontinuities correspond to the binding
energies of the atomic electrons).
When one wishes to model the form of the interaction of a heavy charged particle with atoms, the
energy transferred in the interaction, the kinetic energy, and the exit angle of the secondary electron,
one must know the total cross section and the double differential cross section (of the energy and of the
exit angle) of ionization. Measurements of the double differential cross section of ionization of several
light atoms by protons and electrons were reported in [8-13]. However, the experimental data on the
double differential cross section are incomplete because they neither comprise a large energy range nor
many types of incoming particles. Therefore, in order to calculate the double differential cross section,
the differential cross section of the transferred energy and the total cross sections of ionization, the
theory of binary collisions was used [14-18]. The essence of the theory of binary collisions is that the in-
elastic interaction of a charged particle with an atom is considered as classical scattering at one of the
electrons of the atom; the electron has a momentum and an energy which are given by its state in the atom.
This approximation provides a formula for the scattering cross section which depends upon the particle
parameters before and after the collision. This cross section is then averaged over the probability dis-
tribution of the momentum vector of the atomic electron and its energy, both obtained by quantum mech-
anical methods. When the shell structure of light atoms is properly brought into account, the differential
ionization cross sections over the transferred energy are in good agreement with the corresponding experi-
mental cross sections [19]. An acceptable agreement is obtained only at the maximum of the double differ-
ential cross section for the angular distributions of the outgoing electrons of ionization. The theoretical
cross sections are several dozen times smaller than the experimental cross sections at both small and
large exit angles. At small angles, the discrepancy is partially explained by the fact that for comparable
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velocities of the outgoing electron and, say, the proton, the proton captures the electron in the interaction
region and, at a certain distance from the atom, the electron is emitted in the direction of motion of the
incoming particle. This effect is disregarded in the theory of binary collisions. The authors of [20] have
attempted to include into their considerations the interaction of the incoming proton with the outgoing elec-
tron in the case of the hydrogen atom which was considered within the framework of quantum mechanics.
The result was a coefficient which depends upon the velocity vectors of both the proton and the electron
and with which the double differential cross section must be multiplied in the first Born approximation in
order to obtain better agreement with the experimental results. The correction can be applied to the an-
gular distributions of the outgoing electrons of ionization when the considerations are concerned with atoms
of hydrogen, carbon, nitrogen, and oxygen; the distribution is 'to be calculated with the theory of binary
collisions. It was then possible to significantly improve the agreement with the experimental results at
small angles. For angles exceeding 90?, the calculated cross sections are much smaller than the experi-
mental cross sections and at the present time there exists no theoretical explanation of this fact. But the
calculated cross sections can be used, because at large exit angles the experimental cross sections are
1.5-2 orders of magnitude smaller than the cross sections at the maximum.
When we use a hydrogen-like velocity distribution of the atomic electrons for each subshell of light
atoms, we can derive a final formula for the double differential cross section of ionization of the i-th
subshell:
d2a1
de dig
_0 W tw,i t X LnV 2") f (y; at, (Di, cos 0) X
n(E~lt) (e I lf)xy 1-e vi(e)
X q) (y;,ai, 01, cos 9) dy;
f y? (at+y2)1/2
f (y; at, (Di, cos 9) _ (ai +y2)4 X
X [a2?+(af+ 0?) y2-2ai/2DfyX (at+y2)1/2cos0]-3/2
W (y; at, (Di, cos 0) = at~2y2 sin20-
where vp denotes the velocity of the incoming particle, a.u.; K denotes the velocity of the outgoing electron,
a.u.; B denotes the exit angle of the electron relative to the proton trajectory; E denotes the kinetic energy
of the outgoing electron; Ji denotes the binding energy of the electrons in the i-th subshell; Ni denotes the
number of electrons in the i-th subshell (the number is calculated from the multiplicity of the levels of the
atom); Ei denotes the average energy of the electrons in the i-th subshell; (e + Ji)Ry denotes the energy
transferred, Rydberg units; and
+! . ai/2(y ty2)1/2cos0+'paf(y~ y2)l
P m 2 2
(0) = (vp - 2 vPK cos 0 + K2)112
- vpl,
VP e } 1? 2E? 1/2 (11)
The limits of integration are selected with proper regard for the energy and momentum conservation laws;
the limits of integration are:
1. Cos0 > 0:
a) if Pi > COS 0, then P < Y < y2.f;
b) if 0f < Cos 0, t h e n yi,i Y Y2 t
2. cose I cos0 I, then0 y < -yi.i;
b) if Pi < I cose I,thend&o/de dQ = 0.
Ci C?
yf, i = Ai+Bf ' y2. i = I Ai `Bf
me of 1/2
MP Ai=(1 MPP) ((DI ~ Me ,)1/2.
(( m 2 2
Bt=(DtIcos0IL11-ma) + 4mafisin20] 112
;
P
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CZ-2 m a;-Vsin20)
MP
The binding energies of the electrons and their effective number were calculated from tables of the energy
levels of atoms [21]. The average energies of the electrons were calculated with the method described in
[22]. The values of these parameters are listed in Table 2.
In order to make a comparison with the experimental results, the angular distributions of the elec-
trons were calculated for nitrogen atoms at a proton energy of 1.7 MeV. The comparison is illustrated in
Fig. 3. The experimental cross sections were taken from [13]. For electrons with an energy > 200 eV
and exit angles < 90?, the greatest discrepancy does not exceed 100%. For angles > 90?, the calculated
cross sections are much smaller than the experimental cross sections, as indicated above. It must be
noted that, unless corrections for the interaction of the outgoing proton with the electron knocked off by
the proton are introduced, the calculated cross sections differ from the experimental cross sections
several dozen times at small angles.
Thus, this simple method of calculating the double differential cross section for complicated atoms
allows an improved determination of the angular distribution of the electrons which are emitted in the ioni-
zation of an atom. The simplicity and the rather good agreement with the experimental results at angles
< 90? are the advantages of this calculation method over the quantum mechanical method which has been
worked out only for hydrogen and helium atoms.
After integrating over the exit angle of the electron, one can obtain the differential ionization cross
section as a function of the transmitted energy. The calculations were made for hydrogen, carbon, nitro-
gen, and oxygen atoms and for protons with energies between 0.21 and 14 MeV (step width of the energy
140 keV); the calculations were also made for a particles with energies between 2 and 5.6 MeV. Figure
4 shows as an example the results of calculations for nitrogen and for protons of various energies; it fol-
lows from the curves that the differential ionization cross section in dependence of the transmitted energy
is characterized by discontinuities at energies which are equal to the binding energies of the electrons in
the atoms. Figure 5 shows the ratio of the differential ionization cross section as a function of the kinetic
energy of the emitted electrons (nitrogen atoms), as calculated by the theory of binary collisions and in
the approximation of scattering of free electrons, to the experimental cross section of [13]. The proton
energy is a) 1.0 and b) 0.2 MeV. It follows from the figure that the classical cross section is distinguished
from the experimental cross section particularly at high kinetic energies of the electrons, i. e., at ener-
gies close to the maximum energy. The cross sections calculated with the theory of binary collisions are
in good agreement with the experimental cross sections except for very small and very high energies of
electron emission. For low kinetic energies of the outgoing electrons, one could not expect a good agree-
ment with the experiments, because the experiments were made on molecular nitrogen and this detail was
disregarded. The fact that the classical cross sections are closer to the experimental cross sections at
low energies must be considered a matter of chance, because the cross sections calculated with the theory
of binary collisions are in better agreement with the experimental data. For the purpose of estimating the
classical differential cross sections of ionization, Fig. 6 shows the ratio aTBC/o'CLforprotonsbombarding
hydrogen and nitrogen. It follows from the figure that the cross section of scattering at free electrons can
be used only at very high energies of the outgoing particles (in excess of 7 MeV in the case of hydrogen and
in excess of 10-15 MeV in the case of nitrogen) and for outgoing particle energies which are much greater
than the energy of the atomic bonds.
We used the differential cross sections to calculate the total ionization cross sections, the atomic
stopping power, etc. The agreement with the experiments is not worse than 25%. Figure 1 shows the
total cross sections of the ionization of light atoms by protons of various energies. The symbol (0) indi-
cates the experimental cross sections taken from [23] for hydrogen. The same figure (right scale) depicts
the dependence of the total macroscopical cross section of inelastic interactions of protons with tissue-
equivalent matter upon the proton energy.
The total cross sections of the ionization of hydrogen, nitrogen, and oxygen atoms by electrons can
be calculated with the semi-empirical formulas of [24]; one can use the results of [25] in the case of car-
bon atoms. The results of [25] can also be used to calculate the differential ionization cross sections as
functions of the transmitted energy in the case of electron-induced ionization of atoms. The calculated
differential cross sections of the ionization of atoms by electrons can be described by the approximation
formula
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E Wk J W tac there remain two types of asymptotic solutions:
1. Weak Absorption (LT2 < ET1):
2z
gTi=A-GT1(p) exp(-ET2vTt-4 (Ail+DT2t)) x(A1+DTs1) 1(AI-DTzt)-1 i_2
2. Strong absorption (ET2 > Ti):
E
z
?T; = A+GT1 (p) exp (-Eeff iTt -4 (A II +Deff t)) X (`~ II ?Deff t) - i/2
The functions Gt and the effective parameters Eeff, Deff, A -~, and Al are evaluated explicitly. Thus
Zeff= Er + 'Y (ET2 - ET1; Drin; Tr);
(u; v, u-l-v-V(u-v)2+4' uv
Ya)=r 2(1-Ya)
Ta (au)=2 Dal L K1 (RV(Ea2-6z)/Da2) ]2
QT = ET1; GE= EEIDE2!DE1' 9 = (2.405/R)22.
In the first case a measurement of cpT (t, z) in the inner zone permits the determination of the diffusion
parameter ET2 and LT2 of the outer zone, but not in the second case except for small R when Eeff ET2
and Deff DT2, which was confirmed experimentally.
For a steady point neutron source inside the cylinder the asymptotic z distribution of epithermal
neutrons is determined by the sign of the difference ?E2 - ?E1, where ?ai = fai/Dai:
1. Weak slowing down (?E2 < PEI)
(PEi=B-GEi(P) z exp (-ttEiz -'E2 (z).
2. Strong slowing down (?E2 > ?E1)
Translated from Atomnaya Energiya, Vol. 40, No. 4, p. 332, April, 1976. Original article sub-
mitted May 21, 1975; abstract submitted October 1, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication maybe reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
%'Ei=B*GEi (p) exp (-peff z);
?eff-V?4,+'Y Ez-?E1; YE)
The asymptotic behavior of the stationary thermal neutron flux calculated in the two-group approximation
is determined by which of the quantities ?ai is the smaller; accordingly there are four types of solutions.
Thus for nuclear geophysics the characteristic case is ?E2 min ?ai for which (PTi, ac (1/z) exp (-?E22)
'DT2(z) - 'DE2(z). The result obtained in the few-group approximation
PE' (z) - PTI (z) - (DE2 (z); z> zac; pE2=min
is confirmed by a numerical calculation in the six-group removal-diffusion model. The measurement of
the dependence of qPD and cpri on z permits the determination of the asymptotic neutron relaxation length
in the outer zone of the system.
The transient forms of the distributions have been obtained explicitly for both problems in the re-
gions t 2 tac and z < zac, which include the rapidly decreasing harmonics in addition to 497c; these enable
us to estimate the limiting values of tac and zac.
A comparison of the analytic properties of the spectra of the solutions, the structure of the solutions
for arbitrary values of t and z, and the asymptotic behavior of the nonstationary and stationary problems
shows that for a steady source the z coordinate plays the role of the time t for a pulsed source.
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V. A . D u l i n UDC 621.039.51.12:539.125.52
We present a deviation of the multigroup equation for the neutron importance function relative to
asymptotic power in an integral formulation. The equation describes the spatial and energy distributions
of the importance Vni of neutrons in a heterogeneous reactor [1] in the usual notation.
i M G
/_j 71 1 ~
trn in= 1 1a=
Aa?1Wm kcp h
It is not the same as the adjoint of the equation for a heterogeneous neutron flux in integral form.
In the transition to a homogeneous reactor it describes the homogeneous neutron importance.
The spatial distribution over a cell of the neutron importance averaged over the fission spectrum
was calculated and measured in the BFS-26 and BFS-30 zero-power heterogeneous critical slab reactors
[2].
The measurements were performed by displacing a miniature 252Cf source of spontaneous fission
neutrons perpendicular to the layers of material--and recording the relative level of the asymptotic power.
The measured and calculated results shown in Fig. 1 are in good agreement.
11
In
Fig. 1. Variation of asymptotic
power in the displacement of a
252Cf neutron source normal to
the layers in the heterogeneous
fast critical assemblies a) BFS-
26 and b) BFS-30: 1) C; 2) 235U
- Al; 3) Al; 4) steel; 5) 238 U02;
6) 215U-Al; 7) Na.
Translated from Atomnaya Energiya, Vol. 40, No. 4, p. 333, April, 1976. Original article sub-
mitted January 24, 1975; abstract submitted November 20, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
1. F. Storrer et al., Nucl. Sci. and Engng., 24, 153 (1966).
2. V. A. Dulin et al., in: Proc. of IAEA Symp. on Fast Reactor Physics, Tokyo, Oct. (1973), p. I,
Rep. A-26.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
IN-CORE SYSTEM FOR AUTOMATIC POWER
CONTROL OF IRT-M REACTOR
L. G. Andreev, Yu. I. Kanderov,
M. G. Mitel'man,, N. D. Rozenblyum,
V. P. Chernyshevich, and Yu. M. Shipovskikh
This paper gives developmental results for an in-core system of automatic power control for the
IRT-M reactor and a determination of the metrologic characteristics of the system of in-core detectors
with inertial correctors as compared to extra-core standard ionization chambers. Direct-charge detec-
tors (DCD) with rhodium emitters, which are used in the in-reactor monitoring system (IMS) of the IRT-M
reactor, were used as sensors for the automatic power control system.. The IMS system consists of six
DCD sets arranged along a diameter of the core and each set consists of five commerical type-DPZ-1P
DCD positioned along the height of the core [1].
The DCD is presently the most promising of the in-reactor detectors of energy release for applica-
tion in any reactor [2]. Activation DCD are inertial because of the decay time of the induced isotope, but
the use of simple correctional devices makes it possible to measure neutron flux.density with practically
no inertia [3]. The transfer function W(p) of the correctional device must satisfy the condition
H (P) W (P) = K,
where K is the static transfer factor of the DCD-corrector unit; H(p) is the DCD transfer function; p = d/
dt.
A DCD with rhodium emitter has a great advantage over other types of activation and Compton detec-
tors because of high sensitivity which provides a favorable signal-to-background ratio.
10 t, sec 103 10
Fig. 1. Contribution to reactor energy release from decay of fission products and transient
responses of DCD-corrector and reactor-DCD-corrector units.
Fig. 2. Block diagram of automatic power control system for IRT-M reactor: 1) constant-
current amplifier; 2) corrector; 3) power sensor; 4) power-control amplifier; 5) motor
amplifier with servodrive; 6) direct-charge detector; 7) reactor; 8) automatic control rod.
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 335-337, April, 1976. Original article
submitted December 30, 1975; revision submitted May 19, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
In the construction of an automatic control system,
it is necessary to take into account the inertial nature of
energy release associated with the delay of heat release
from the decay of fission products. The time dependence
of relative energy release [4] for a stable number of fis-
sions is given by curve 1 in Fig. 1, which indicates that
the power of the reactor increases for a considerable
length of time after the reactor reaches a stable operating
'" qgo I mode because of the decay of fission products; the in-
Fig. 3. Comparison of IC and DCD cur- tween the decay law for the isotope 104mRh and the law for
rent over a weekly operating cycle of IRT- variation of energy release after a step change in neutron
M reactor: x) total DCD current; 0) IC flux density. Curve 2 gives the transient response of a
current, rhodium DCD with an inertial corrector which corrects
for the inertial characteristics caused by the formation
of 104Rh.
The transient response of the react or-D CD- corrector unit, where the DCD with corrector serves as
a detector of energy release, is given by curve 3 and differs from the ideal by no more than 3%.
A block diagram of the system developed for automatic reactor power control is shown in Fig. 2.
A constant-current preamplifier amplifies the DCD current and matches the input potential of the inertial
corrector to the DCD. Power sensors were assembled from K2UT402 microcircuits. A KSP-4 recorder
and N-700 loop oscillograph were used to monitor power. A comparison of readings, normalized at the
45 MW
crease amounts to 7?/0. For noninertial measurement of
reactor power, therefore, a corrector is required with a
transfer function S(p) satisfying the condition D(p)S(p) = K
where D (p) is the transfer function of the reactor. This
paper gives an approximation based on the similarity be-
2,1
oko?ao
2,9
1,25
aow
0 0,2
Fig. 4
Fig. 4. Readings from IC (0) and DCD-corrector unit (X) when rods of safety and
control systems were dropped into the core.
Fig. 5. Readings from IC (0) and DCD-corrector unit (X) during control of reac-
tor power by DCD-corrector.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
maximum, from an in-core DCD and from an external KNK-53 ionization chamber (IC) used operationally
for power determination in a stable operating mode of the reactor is shown in Fig. 3 which indicates that
for constant reactor thermal power, the readings of the IC varied by 17% over 120 h of operation while the
readings of the DCD remained practically constant. The actual change in the IC sensitivity as a sensor
for power control was associated with shifting of compensating rods; it is therefore preferable to use in-
core DCD as power sensors. The time characteristics of the DCD-inertial corrector unit and of an ioniza-
tion chamber were compared. For this purpose, the safety and compensating rods were dropped into the
reactor core and the readings from DCD-corrector and IC displayed on the loop oscillograph. Results of
the measurements, normalized at the maximum, are shown in Fig. 4. Analysis of transient processes
during rapid introduction of negative reactivity showed that the inertia of the DCD-corrector unit was no
worse than the IC inertia in the relative signal range 0.05-1.0. IC inertia, which is determined by the
time constant with the capacity of connecting wires and the load resistance included along with neutron
transit time to the IC, is (1-10). 10-3 sec. The discrepancy between DCD and IC readings at relative sig-
nal values < 0.05 is explained by the inertia of energy release not measured by the IC. The equipment was
tested in the automatic power control mode (see Fig. 2). In this case, the total current readings from
DCD and IC were compared. The time dependence of DCD and IC readings is shown in Fig. 5 for different
thermal powers of the reactor and indicates that regulation was effective in the power range 0.5-3.5 MW.
The authors are grateful to B. K. Ignatov for discussion of the work and continued interest in it and
to V. M. Vertogradskii for help in some of the experiments.
1. Direct-Charge Detectors, Technical Specifications TU16-538, 243-74 [in Russian].
2. M. G. Mitel'man et al., in: Metrology of Neutron Radiation at-Reactors and Accelerators [in Rus-
sian], Vol. 1, Izd. Standartov, Moscow (1972), p. 115.
3. N. D. Rozenblyum et al., in: Dosimetry of Intense Fluxes of Ionizing Radiation [in Russian],. Fan,
Tashkent (1969), p. 130.
4. A. M. Weinberg and E. P. Wigner, Physical Theory of Neutron Chain Reactors, Univ. of Chicago
Press (1958).
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
DETERMINATION OF IRRADIATION TEMPERATURE
FROM MEASUREMENT OF LATTICE CONSTANT OF
RADIATION VOIDS
Y. V. Konobeev UDC 621.039.531:669.45
A method was proposed [1] for the determination of irradiation temperature in those parts of a fast-
neutron reactor in which the placement of thermocouples or other temperature indicators was impossible
for one reason or another. The method was based on the high sensitivity to irradiation temperature of the
lattice constant of the body-centered cubic (bcc) lattice of voids in molybdenum and other heat-resistant
metals produced, as is well known, in these materials after irradiation by neutron fluxes of 1022 neutrons/
cm2 (E > 0.1 MeV) and measured by transmission electron microscopy. The following relation between the
void lattice constant aL and the absolute irradiation temperature T was proposed [1]:
aL=aT; a=0.32 ?K. (1)
A comparison between values of aL calculated from Eq. (1) and experimental values (Table 1) demon-
strates the poor description of experimental data for molybdenum irradiated in a reactor at elevated tem-
peratures. Somewhat better agreement with experiment can be obtained if one uses the relation NV -
exp(-PT) [2] to describe the temperature behavior of void concentration in irradiated metals and considers
that NV and a L are connected through the relation NV = 2/ a L for a bcc lattice. Table 1 gives values of
a L calculated from the relation
aL = 54.57 exp ( (2)
530.79
which was arrived at by least-square analysis of the experimental data. For Tirr = 1000?C, the calculated
value of GL differs from the experimental value by an amount which considerably exceeds the error in
measurement of aL (Table 1).
The purpose of this report is to show that existing data for a L in molybdenum are well described by
the relation
TABLE 1. Experimental and Calculated
Values of Void Lattice Constant in Molyb-
denum Irradiated by Fast Neutrons
Void lattice constant, 9
,
T
Reactor
experi-
calculated from Eq.
C
ura
mental
aL, ~i
(1) I
(2) I
(3)
430
EBR-11
220 [2]
225
205
221
580
EBR-11
270 [2]
272
272
268
585
EBR-11
265 [3]
275
274
270
640
IDFR
300 [4]
292
304
293
680
EBR-11
320 [2]
305
328
312
800
EBR-11
390-410 [2]
343
412
390
900
EBR-11
470[2]
375,
497
491
1000
EBR-11
660[2]
407
600
664
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 337-338, April, 1976. Original article
submitted July 16, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
3558?K
aL=121 A 1558?K-T
The critical temperature Tc = 1558?K = 0.52Tf coincides with the upper temperature limit for the
existence of vacancy porosity in heat-resistant metals. Equation (3) may indicate the existence of a spe-
cial phase transition associated with the formation of a spatial void lattice. According to Eq. (3), the
void concentration should depend on irradiation temperature in the following manner,
N?- (T-7,?T )s (4)
and reach a maximum value of 1.1 .1018 CM -3 for molybdenum when T -- 0. For further verification of Eqs.
(2) and (3), there is particular interest in data for aL at elevated temperatures in the range from 0.44 Tf
to 0.52 Tf.
LITERATURE CITED
1. J. Moteff and V. Sikka, Trans. Amer. Nucl. Soc., 16, 97 (1973).
2. V. Sikka and J. Moteff, J. Nucl. Mater., 54, 325 (1974).
3. F. Wiffen, in: Proc. AEC Symp. Radiation-Induced Voids in Metals, New York, June 9-11, 1971, p.
386.
4. B. Eyre and A. Bartlett, J. Nuc. Mater., 47, 143 (1973).
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
SLOWING DOWN OF RESONANCE NEUTRONS
D. A. Kozhevnikov UDC 539.125.5.174.162.3:539.125.5.162.3
Penetration of a Neutron Pulse through Resonances in the Scattering and Absorption Cross Sections.
In neutron slowing-down theory an analytic expression for the Green's function of the nonstationary trans-
port equation has been obtained in only three cases: a) as(E) = const, as (E) = const; b) as (E) = const,
as (E) - 1/v; c) as - 1/v, ou - 1/v [1]. The last case has no practical application. The most interesting
problem is the study of the nonstationary neutron distribution in matter, taking account of the resonance
structure of the interaction cross sections. In the present paper we give an analytic solution of this gen-
eral problem based on the use of the "causal" form of the central limit theorem.
The energy - time neutron distribution function in matter of arbitrary composition for an arbitrary
energy dependence of the interaction cross sections is found by solving the generalized Weinberg -Wigner
- Corngold- Orlov equation* by the method of spectral approximations and has the following integral rep-
resentation [3]:
Q+ioo
1Vo (t, u)= 2ni Apo (s, u) est ds
a-im
sh (u') T (u')+g (u') [1+si (u')] ski (s, u) du'
[i+s-t (u')] 11-6?;1 (s, ui)] x g(u')
u+
u+ is the initial lethargy, h(u) = 1 - g(u) is the total scattering probability, r (u) is the mean free time,
00(s, u+) is the transform of the Green's function of the nonstationary one-velocity transport equation, and
the quantities T (u), i;1 (u), and ~1(s, u) are defined by Eqs. (8), (9), and (19) respectively of [3].
To take account of the resonance structure of the cross sections we divide the slowing-down interval
[u+, u] into a sufficiently large number N of appropriate subintervals [uk_1, uk], 1 < k < N, uN = u such
that in each of them the scattering and absorption cross sections can be considered constant. Then
N
A (s, u) = E Ak (s),
k=1
and we can write (2) in the form
*This equation is one of the exact noncanonical forms of the transport equation [2].
Translated from Atomnaya Energiya, Vol. 40, No. 4, pp. 338-339, April, 1976. Original article
submitted January 8, 1975; revision submitted November 11, 1975.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
'N (u) *) (s, u+) aA (s, u)
Vo(s, u)=11+ST(u)] [1-8~1(s, u)]
V0 (u) = h (u+) exp r - ~ g (u') du ] ;
U
. (u) L U+ 1 (u') J
si (s, u)= ^-1 [~Si (s, u)-Ef (u)];
(u)
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 Declassified and Approved For Release 2013/04/10: CIA-RDP10-02196R000700070004-7
where fo(s) = 'Po (s, u+); fk (S) =e nk (o), 1